I had the same problem with a Dell computer. The pointer was slightly jumping while touching the touchpad without moving the finger, and sometime even without touching it, while writing. It took me while to figure out that they were (at least) 2 issues (I wasted my time reinstalling/updating drivers etc.)
Troubleshooting:
● The first problem is a badly design Dell laptop: I have 2 computers, a cheap one from Dell, and an expensive one. Both are connected to the same wall outlet, on the same office, but only one of them (the cheap one) has an issue with the touchpad.
● So the second problem was an interference. You can check with a friend which appliance is responsible for that interference by unplugging everything (hopefully it won't be your neighbor device...). And then plug them back each device one by one, while pressing the mouse without moving your finger to see when it will start jumping again. The problem came from an electric blanket or it's cheap charger. (Interestingly the cursor was jumping when we moved at some place of the room...)
(I first thought they were some tiny leak of current going through the ground from a faulty device but no: disconnecting the faulty device from the ground did not solve the problem).
Solution:
This solution to touch the cable did not work for me, I guess this one might work (did not tried yet) but since I'm not interested to disassemble my laptop Roreru's answer looks the more promising, but I don't know how he did. I'll post a picture when I'll time to do it.
Roreru:
I used a piece of thicker aluminum foil from a sealer of a ground
coffee container. Then I managed to open one of the plastic covers at
the bottom of the laptop, and secure the aluminum sheet with one screw
inside the cover. Then I bend the aluminum sheet to have an exposed
surface outside. Finally, I secured the edges with electric tape. This
creates a permanent grounding surface that can be touched by hand or my
lap.