The tAra gItA is from the KiShkindhA kANDa of the adhyAtma rAmAyaNa. The adhyAtma rAmAyaNa is said to be very popular among the followers of the Saint Ramananda who preached ShrI RAmAnujAchArya's teachings in Northern India and promoted rAma-bhakti. This has led some modern scholars to suspect that the adhyAtma rAmAyaNa was actually written by Ramananda himself and was added to the BrahmANDa purANa. But this is hard to justify, without finding out more about what Ramananda's beliefs were. Some of the ideas in this rAmAyaNa clearly are in conflict with RAmAnuja's, for example, those of mAyA, the mithyAtva of saMsAra which is like a dream, and so on. The only other place where I can find these ideas so clearly expressed is in the ShrImad BhAgavata purANa. It is very possible, in my opinion, that the author of the adhyAtma rAmAyaNa was influenced by the BhAgavata. One example, where both are very similar is the birth of rAma/krishNa. The BhAgavata says that kriShNa was born as the four-armed ViShNu Himself. In the adhyAtma rAmAyaNa, rAma is born similarly, not as a normal human child, but as the four-armed ViShNu with all His paraphernalia. KausalyA then offers prayers to Him and only later does He assume the form of a normal human infant.