You can fashion a logic detect from CMOS gates or such. Bear in mind that you have four things to detect:
- high-Z (undriven)
- static low
- static high
- changing signal
There's plenty of examples of handmade 'logic probes' that can do some or all of these things. I'll leave that up to you and your favorite search engine.
Fortunately, pre-made logic probes are widely available at reasonable cost ($10 - $30). These pen-like probes are powered by your board and indicate all four conditions: high-Z, fixed high, fixed low, and pulsing. I've used them, and in my experience they're a handy item to have for board-level troubleshooting. More here: https://www.electronics-notes.com/articles/test-methods/logic-probes/what-is-a-logic-probe.php
Moving up the food chain, you can also get USB-based logic analyzers for your PC. More about those here: https://hackaday.com/2017/07/29/everything-you-need-to-know-about-logic-probes (note: they're calling the thing a 'logic probe', but it's really a logic analyzer.) These are far less expensive than a 'scope and for some work (like I2C, SPI and other protocols) much more useful. Here's an analyzer for less than $20.
If you have a bit more budget, consider a USB-based scope. Then you can look for some basic signal issues if that's a concern (might be for 12MHz.)
Finally, how about a combo 'scope, logic analyzer, pattern generator, and power supply: https://digilent.com/shop/analog-discovery-3/