Related answer together with the posts linked therein. You may want to flip the signs of $a$ and $q$ (here) for easier comparison. The condition $ab=q$ is preserved under that substitution. To summarize: Yes, and Nicco's cfrac is an instance of entry 11 (not 12) that for $ab=q$ can be simplified to a theta quotient like entry 12. I suppose Ramanujan was aware of that, but sought a cfrac that was not restricted to $ab=q$, and entry 12 was the result. I hesitate to make an answer out of this, as I have already written four related posts on MSE.