What to do with an unfinished research project you previously worked on?
I think this question is difficult to answer without knowing the details of the project, and it's really something you should work out with your advisor. But let me offer two perspectives here that maybe helpful. First, you said that you have spent several months on the project. On the grand scheme of things, several months is nothing. A successful project from start to finish can take 1-2 years (and oftentimes even more). So if I were you I would not fret too much about the time lost to the project, should you choose to simply move on.

Secondly, have you heard of the concept of sunk cost? It's basically an economic concept referring to effort/time/capital spent that cannot be recovered. And the key here is that sunk cost should not factor into future decisions. What is lost is lost, and the irrational desire to recover what is unrecoverable usually leads to more lost time and effort. So you should try to evaluate the merit of the project independent of how much time you've spent. If you find it hard to sell the project even to yourself, as you wrote, then maybe it's time to move on.