Was Buddhism ever predominant in Tamil Nadu? Which Buddhism? And when?

After my last post on the disappearance of Buddhism from South India, I received two emails of readers pointing to the fact that Buddhism must have been prosperous in Tamil Nadu, given that Dharmakīrti himself was born in Tamil Nadu and that the Maṇimēkalai (a Buddhist literary text in Tamil, datable perhaps to the 5th–7th c.) presupposes a Buddhist community and reuses materials from Śaṅkarasvāmin’s Nyāyapraveśa.

In fact, most of us learnt in their early years of study of Classical Indology (broadly construed, so that it should cover the intellectual production of South Asia, from Śrī Laṅkā to Tibet, from Pāli to Sanskrit, Classical Tamil, Classical Tibetan, etc.) that Buddhism had become influential in Tamil Nadu, at least from the time of Amaravati onwards. When one looks closer at the data, however, the findings are less clear.
Concerning the timeline of Buddhism in Tamil Nadu:

• First of all, the findings appear to indicate clearly a decline and then disappearance of Buddhism in the early second millennium AD (see this post).
• I could not find any information concerning clear evidences of an institutional presence of Buddhism before the 4th c. AD. This does not exclude that there might have been people who considered themselves Buddhists, but they did not leave trace of their belief.

Concerning the type of Buddhism,

• Petra Kieffer-Pülz (see her comment here) showed us evidence of the presence of Theravāda Buddhists using Pali as medium in Tamil Nadu from an earlier (perhaps already 3rd c.) until a late age (13th c.). Further evidences about their presence can be found also in Schalk’s work (see the same post).
• Schalk (see the same post) gathered informations regarding syncretic Buddhism.
• The Maṇimēkalai (see above) reuses materials from the early Pramāṇavāda school.

Thus, it lies beyond question that there were Theravāda and Mahāyāna Buddhists in Tamil Nadu, at least from the 4th c. until their decline in the 12th–13th c.

But what do the Maṇimēkalai and the place of birth of Dharmakīrti (or of Bodhidharma) tell us about the fortune of Pramāṇavāda in Tamil Nadu? Not so much, I think. In fact, even if Dharmakīrti were really born in Tamil Nadu (in order to assert this with safety we should be able to determine that Tibetan historians clearly meant Tamil Nadu when they spoke of, e.g., yul lho phyogs), he left his place of origin very early in his life and does not seem to have left anything comparable to Nalanda in Tamil Nadu.

As for the Maṇimēkalai, the fact that it reuses a relatively easy manual on Buddhist logic does not seem to me to mean anything more than that the Nyāyapraveśa was easy enough to be used by a wide number of readers (and it was in fact used by Jaina and even “Hindu” authors, see Tachikawa 1971).

Once again, I am sorry to admit that I do not read Tamil. Thus, on the Manimekalai I rely entirely on secondary literature (especially Anne Monius, Paula Richman and the contributions in the volume edited by Peter Schalk, A Buddhist woman’s path to enlightenment).