I've had the exact same problem with finding the rare cave critters.
I had luck with flying into space, landing on the opposite side of the planet, then searching caves after that.
Sometimes they just really are hard to find and it will take you a while before you get lucky.

Everyone has problems finding Rare Underground critters quickly. Pure RNG Gods.

For this reason, many players do not put ANY extra effort into completing the Scanned Creatures / Zoology goal for a planet, if they read that it has a required rare, underground creature listed.

It is best to just move on if you are not finding a last critter. The galaxy is huge so you will not run out of systems to explore and you can often 100% fauna three planets in the time it will take you to maybe find that one holdout where you are.

I usually give it a day/night cycle max before calling the code and moving on. The only tip for finding a cave based critter is to check a series of POIs near caves. As often as not, I find them at the entrances of the cave versus inside. Traveling a quarter way around the planet can be helpful. The rules of RNG spawn for critters is not known but in some cases it can be a particular region of a planet at a particular time of day....so it can take a long time for all the elements to align if you are searching.

Building a base always seems to work for me in those situations (it is just a matter of whether it is base worthy). There are some cases where you have 10+ critters where the nanite reward might make it worthwhile to do that.

I think you can just wait for a underground animal to appear. Find a cave of some size, and just stand in place and wait for a bit. The animal should spawn in after a while.