I want to try to write what I think to your discussion.
On page 43 in Bhikkhu Bodhi’s book, he lists the unwholesome-resultant cittas, the wholesome- resultant cittas and the functional cittas that comprise all the rootless cittas.
In the unwholesome-vipaka list, there are the 5 that lead to the 5 senses- event that Lal list in his article. Then there are two more unwholesome-resultants, the receiving and investigating consciousness.
I think the name for these is referring to their function, as in “receiving consciousness” does the job of “receiving” in a Citta vitthi. But not necessarily, I think, because there is a list at page 127, that you also refer to already, where it is explained in more detail.
The same holds for the wholesome-vipakas, here there is a whole-some vipaka citta called “investigating consciousness” (with equanimity, and also with joy).
I think the citta that you refer to in this discussion should be the citta Nr. 19 (unwholesome investigating consciousness accompanied by equanimity) as well as citta number 26 (wholesome investigating consciousness acc. by equanimity).
On page 127, it is shown that these two cittas can perform the function of “Rebirth, bhavanga, death”. Since the bhavanga state is not equal to the bhavanga citta, and the former is not a citta but the latter is (that is why Asanna does not have any citta arising except for the last moments) here what Bhikkhu Bodhi means with “bhavanga” as a function we can understand it as the “Arrest bhavanga” and “Vibrational bhavanga” which are cittas that preceed the Mind-Door Adverting consciousness “M” in a Mind-Door Process, see page 166.
I appreciate your feedback on this idea.