The connection stems a lot from "who the Pallavas even were originally" (not a named dynasty of the Tamils of yore - the Pandyas, Cheras and the Cholas)....and the concurrent Brahmi script arc for North and South.
Or as we Tamils often like to call Pallavas....affectionately as "the" Kanchi dynasty (their great capital was at Kanchipuram)
The Pali canon, Hindu epics and other immense cultural export by the Pallavas hugely influenced a large number of South East Asian scripts too.
Have a look at Burmese, Thai, Khmer, Javanese, Balinese, and old Malay script (Kawi) too when you have a chance.
In old Tamil movie song, we have MGR as "the" great Pallava emperor reflecting on sad divide arising with his sister (w.r.t another kingdom)..... and it moves the heart
"oru kodiyil, iru malargal....pirandhadhamma pirandhadhamama?...annan thangai uravu murai.....malarndhadhamma malarndhadhamma?"
one flag (branch), two flowers.... born (together)? x2
older brother, younger sister....that close bond....must bloom (surely in the end)? x2
And so that very same thing is seen in the Pallava language tree and its progeny today.
You Bongs have a very fine language too. But in end for me, nothing compares to Tamil, even when I look as objectively and neutrally as possible (I know quite a fair few number to compare across some divides).....simply we have the best one