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This version of the script incorporates providing input for buffer/stack on command line, and option for display of current buffer/stack contents. Also provides return code which might be used for decision on whether contents requiring "processing" are still in buffer or not.

#!/bin/bash
    
Push=0
Pop=0
Display=0
fifo=1 ; mode="FIFO"    ### DEFAULT
lifo=0
dataline=""

while [ $# -gt 0 ]
do
    case $1 in
        --push ) Push=1 ; Pop=0 ; shift ;;
        --pop ) Pop=1 ; Push=0 ; shift ;;
        --show ) Push=0; Pop=0 ; Display=1 ; shift ;;
        --fifo ) fifo=1 ; lifo=0 ; mode="FIFO" ; shift ;;   ### Buffer MODE
        --lifo ) lifo=1 ; fifo=0 ; mode="LIFO" ; shift ;;   ### Stack MODE
        -- ) shift ; dataline=${@} ; break ;;
        * ) echo -e "\n Invalid parameter used on command line.  Only valid options: [ --push | --pop ]\n Bye!\n" ; exit 1 ;;
    esac
done

if [ ${Display} -eq 1 ]
then
    if [ ${fifo} -eq 1 ]
    then
        if [ -f FIFO.txt ]
        then
            if [ -s FIFO.txt ]
            then
                wc -l FIFO.txt >&2
                echo -e "Hit return to view contents ...\c" >&2 ; read k <&2
                more FIFO.txt
                RC=98
            else
                echo -e "\n FIFO buffer is empty at this time.\n" >&2
                RC=0
            fi
        else
            echo -e "\n FIFO buffer does not exist.\n" >&2
            RC=99
        fi
    fi
    if [ ${lifo} -eq 1 ]
    then
        if [ -f LIFO.txt ]
        then
            if [ -s LIFO.txt ]
            then
                wc -l LIFO.txt >&2
                echo -e "Hit return to view contents ...\c" >&2 ; read k <&2
                more LIFO.txt
                RC=98
            else
                echo -e "\n LIFO buffer is empty at this time.\n" >&2
                RC=0
            fi
        else
            echo -e "\n LIFO buffer does not exist.\n" >&2
            RC=99
        fi
    fi
    exit ${RC}
fi

if [ ${Push} -eq 1 -a -z "${dataline}" ]
then
    echo -e "\n ERROR: did not provide data for capture in BUFFER/STACK\n Bye!\n" ; exit 1
fi

if [ ${Push} -eq 0 -a ${Pop} -eq 0 ]
then
    echo -e "\n ERROR: must specify one of the two stack operations: --push or --pop \n Bye!\n" >&2 ; exit 1
fi

stack="${mode}.txt";
tmp="${mode}.tmp"
if [ ! -f "${stack}" ] ; then touch "${stack}" ; fi

if [ ${Push} -eq 1 ]
then
    # put a new line into FIFO/LIFO
    echo "${dataline}" >> "${stack}"
    wc -l "${stack}" >&2
fi

if [ ${Pop} -eq 1 ]
then
    if [ -s "${stack}" ]
    then
        #get line back from FIFO
        if [ ${fifo} -eq 1 ]
        then
            head -n1 "${stack}"
            sed --in-place '1d' "${stack}"
            wc -l "${stack}" >&2
        else
            tail -n1 "${stack}"
            sed --in-place '$d' "${stack}"
            wc -l "${stack}" >&2
        fi
    else
        echo -e "\t ERROR: attempt to pop line from EMPTY stack.\n" >&2
        exit 1
    fi
fi

#!/bin/bash

if [ $# -eq 0 ] ; then  echo -e "\n ERROR: must specify one of the two stack operations: --push or --pop \n Bye!\n" ; exit 1 ; fi

fifo_stack="fifo.txt";
fifo_tmp="fifo.tmp"

Push=0
Pop=0
fifo=1
lifo=0

while [ $# -gt 0 ]
do
    case $1 in
        --push ) Push=1 ; shift ;;
        --pop ) Pop=1 ; shift ;;
        --fifo ) fifo=1 ; lifo=0 ; shift ;; ### Buffer MODE
        --lifo ) lifo=1 ; fifo=0 ; shift ;; ### Stack MODE
        * ) echo -e "\n Invalid parameter used on command line.  Only valid options: [ --push | --pop ]\n Bye!\n" ; exit 1 ;;
    esac
done

i=$(( $(wc -l "${fifo_stack}" | awk '{ print $1 }' ) + 1 ))

if [ ${Push} -eq 1 ]
then
    # put a new line into FIFO
    echo "append to FIFO - line ${i}" >> "${fifo_stack}"
    wc -l "${fifo_stack}"
fi

if [ ${Pop} -eq 1 ]
then
    if [ -s "${fifo_stack}" ]
    then
        #get line back from FIFO
        if [ ${fifo} -eq 1 ]
        then
            echo $(head -n1 "${fifo_stack}" )
            tail -n +2 "${fifo_stack}" > "${fifo_tmp}" && mv "${fifo_tmp}" "${fifo_stack}"
            wc -l "${fifo_stack}"
        else
            echo $(tail -n1 "${fifo_stack}" )
            tac "${fifo_stack}" | tail -n +2 | tac > "${fifo_tmp}" && mv "${fifo_tmp}" "${fifo_stack}"
            wc -l "${fifo_stack}"
        fi
    else
        echo -e "\t ERROR: attempt to pop line from EMPTY stack.\n" >&2
        exit 1
    fi
fi

As for removing the first line from the stack/buffer file from the file in-place, that would be a task for sed. I am not a jedi-master of sed, so am not able to offer a specific solution at this time, but I will research that further and come back with an edit to this answer.

me@OasisMega1:/0__WORK$ ./test_129.sh --push -fifo
1 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --push -fifo
2 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --push -fifo
3 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --push -fifo
4 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop -fifo
append to FIFO - line 1
3 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop -fifo
append to FIFO - line 2
2 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop -fifo
append to FIFO - line 3
1 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop -fifo
append to FIFO - line 4
0 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop -fifo
     ERROR: attempt to pop line from EMPTY stack.
me@OasisMega1:/0__WORK$

As for removing the first/last line from the stack/buffer file from the file in-place, that would be a task for sed.

I was able to identify the logic for deleting the first/last line depending on fifo/lifo mode using very simple sed directives. That is implemented in the below script.

#!/bin/bash

Push=0
Pop=0
fifo=1 ; mode="fifo"    ### DEFAULT
lifo=0

while [ $# -gt 0 ]
do
    case $1 in
        --push ) Push=1 ; Pop=0 ; shift ;;
        --pop ) Pop=1 ; Push=0 ; shift ;;
        --fifo ) fifo=1 ; lifo=0 ; mode="fifo" ; shift ;;   ### Buffer MODE
        --lifo ) lifo=1 ; fifo=0 ; mode="lifo" ; shift ;;   ### Stack MODE
        * ) echo -e "\n Invalid parameter used on command line.  Only valid options: [ --push | --pop ]\n Bye!\n" ; exit 1 ;;
    esac
done

if [ ${Push} -eq 0 -a ${Pop} -eq 0 ]
then
    echo -e "\n ERROR: must specify one of the two stack operations: --push or --pop \n Bye!\n" ; exit 1
fi

stack="${mode}.txt";
tmp="${mode}.tmp"
if [ ! -f "${stack}" ] ; then touch "${stack}" ; fi

i=$(( $(wc -l "${stack}" | awk '{ print $1 }' ) + 1 ))

if [ ${Push} -eq 1 ]
then
    # put a new line into FIFO/LIFO
    echo "append to FIFO - line ${i}" >> "${stack}"
    wc -l "${stack}"
fi

if [ ${Pop} -eq 1 ]
then
    if [ -s "${stack}" ]
    then
        #get line back from FIFO
        if [ ${fifo} -eq 1 ]
        then
            head -n1 "${stack}"
            sed --in-place '1d' "${stack}"
            wc -l "${stack}"
        else
            tail -n1 "${stack}"
            sed --in-place '$d' "${stack}"
            wc -l "${stack}"
        fi
    else
        echo -e "\t ERROR: attempt to pop line from EMPTY stack.\n" >&2
        exit 1
    fi
fi

me@OasisMega1:/0__WORK$ ./test_129.sh --push -fifo
1 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --push -fifo
2 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --push -fifo
3 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --push -fifo
4 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop -fifo
append to FIFO - line 1
3 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop -fifo
append to FIFO - line 2
2 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop -fifo
append to FIFO - line 3
1 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop -fifo
append to FIFO - line 4
0 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop -fifo
     ERROR: attempt to pop line from EMPTY stack.
me@OasisMega1:/0__WORK$

Session log for LIFO mode is as follows:

me@OasisMega1:0__WORK$ ./test_129.sh --push --lifo
1 lifo.txt
me@OasisMega1:0__WORK$ ./test_129.sh --push --lifo
2 lifo.txt
me@OasisMega1:0__WORK$ ./test_129.sh --push --lifo
3 lifo.txt
me@OasisMega1:0__WORK$ ./test_129.sh --push --lifo
4 lifo.txt
me@OasisMega1:0__WORK$ ./test_129.sh --pop --lifo
append to FIFO - line 4
3 lifo.txt
me@OasisMega1:0__WORK$ ./test_129.sh --pop --lifo
append to FIFO - line 3
2 lifo.txt
me@OasisMega1:0__WORK$ ./test_129.sh --pop --lifo
append to FIFO - line 2
1 lifo.txt
me@OasisMega1:0__WORK$ ./test_129.sh --pop --lifo
append to FIFO - line 1
0 lifo.txt
me@OasisMega1:0__WORK$ ./test_129.sh --pop --lifo
     ERROR: attempt to pop line from EMPTY stack.

me@OasisMega1:0__WORK$ 

#!/bin/bash

if [ $# -eq 0 ] ; then  echo -e "\n ERROR: must specify one of the two stack operations: --push or --pop \n Bye!\n" ; exit 1 ; fi

fifo_stack="fifo.txt";
fifo_tmp="fifo.tmp"

Push=0
Pop=0

while [ $# -gt 0 ]
do
    case $1 in
        --push ) Push=1 ; shift ;;
        --pop ) Pop=1 ; shift ;;
        * ) echo -e "\n Invalid parameter used on command line.  Only valid options: [ --push | --pop ]\n Bye!\n" ; exit 1 ;;
    esac
done

i=$(( $(wc -l "${fifo_stack}" | awk '{ print $1 }' ) + 1 )) 2>>/dev/null

if [ ${Push} -eq 1 ]
then
    # put a new line into FIFO
    echo "append to FIFO - line ${i}" >> "${fifo_stack}"
    wc -l "${fifo_stack}" >&2
fi

if [ ${Pop} -eq 1 ]
then
    if [ -s "${fifo_stack}" ]
    then
        #get line back from FIFO
        echo $(head -n1 "${fifo_stack}" )
        tail -n +2 "${fifo_stack}" > "${fifo_tmp}" && mv "${fifo_tmp}" "${fifo_stack}"
        wc -l "${fifo_stack}" >&2
    else
        echo -e "\t ERROR: attempt to pop line from EMPTY stack.\n" >&2
        exit 1
    fi
fi

me@OasisMega1:/0__WORK$ ./test_129.sh --push
1 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --push
2 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --push
3 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --push
4 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop
append to FIFO - line 1
3 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop
append to FIFO - line 2
2 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop
append to FIFO - line 3
1 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop
append to FIFO - line 4
0 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop
     ERROR: attempt to pop line from EMPTY stack.
me@OasisMega1:/0__WORK$

#!/bin/bash

if [ $# -eq 0 ] ; then  echo -e "\n ERROR: must specify one of the two stack operations: --push or --pop \n Bye!\n" ; exit 1 ; fi

fifo_stack="fifo.txt";
fifo_tmp="fifo.tmp"

Push=0
Pop=0
fifo=1
lifo=0

while [ $# -gt 0 ]
do
    case $1 in
        --push ) Push=1 ; shift ;;
        --pop ) Pop=1 ; shift ;;
        --fifo ) fifo=1 ; lifo=0 ; shift ;; ### Buffer MODE
        --lifo ) lifo=1 ; fifo=0 ; shift ;; ### Stack MODE
        * ) echo -e "\n Invalid parameter used on command line.  Only valid options: [ --push | --pop ]\n Bye!\n" ; exit 1 ;;
    esac
done

i=$(( $(wc -l "${fifo_stack}" | awk '{ print $1 }' ) + 1 ))

if [ ${Push} -eq 1 ]
then
    # put a new line into FIFO
    echo "append to FIFO - line ${i}" >> "${fifo_stack}"
    wc -l "${fifo_stack}"
fi

if [ ${Pop} -eq 1 ]
then
    if [ -s "${fifo_stack}" ]
    then
        #get line back from FIFO
        if [ ${fifo} -eq 1 ]
        then
            echo $(head -n1 "${fifo_stack}" )
            tail -n +2 "${fifo_stack}" > "${fifo_tmp}" && mv "${fifo_tmp}" "${fifo_stack}"
            wc -l "${fifo_stack}" 
        else
            echo $(tail -n1 "${fifo_stack}" )
            tac "${fifo_stack}" | tail -n +2 | tac > "${fifo_tmp}" && mv "${fifo_tmp}" "${fifo_stack}"
            wc -l "${fifo_stack}"
        fi
    else
        echo -e "\t ERROR: attempt to pop line from EMPTY stack.\n" >&2
        exit 1
    fi
fi

me@OasisMega1:/0__WORK$ ./test_129.sh --push -fifo
1 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --push -fifo
2 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --push -fifo
3 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --push -fifo
4 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop -fifo
append to FIFO - line 1
3 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop -fifo
append to FIFO - line 2
2 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop -fifo
append to FIFO - line 3
1 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop -fifo
append to FIFO - line 4
0 fifo.txt
me@OasisMega1:/0__WORK$ ./test_129.sh --pop -fifo
     ERROR: attempt to pop line from EMPTY stack.
me@OasisMega1:/0__WORK$