Mate, I never claimed to be an expert on the subject but just stating very basic facts obtained directly through observation.
Pakistanis look pretty ethnically diverse to me too and has an assortment of languages to boot as well....its not really an argument to apply to one and not the other.
Heck even Nepal has massive variances in appearances, languages, customs etc etc....but underlying connection to a root national culture is much more nuanced thing is it not?...certainly not something to micromanage the slippery slope argument of nationalism at some deeper than today resolution on.
There are threads in this forum about Indian muslims being labelled as all kind of words I will not repeat here, simply because they are not "resisting" the larger national/cultural matrix of today's India "enough" (as judged by non-Indians ironically).
Compared to that South Indians are "resisting" even tinier fraction of it, and you can find such "resistance" to "India" even among North Indian Hindus at various levels anyway... point is its statistically insignificant. Tamil and South Indian culture, just like Bengali, Marathi, North Eastern, Gangetic etc etc cultures have their buffer spaces to co-exist and be stable (example of there being how TN overall peacefully pushed for and got recognition of its own language to remain the sole dominant one in the state, rather than synthesizing Hindi into it)...there is no massive overriding pressure to conform and be micromanaged to a narrow authoritarian concept of "India" being concocted here.
Level of north indians living in South Indian cities and vice versa (and same for bengalis or pretty much anyone else) is a clear testament to that......just like that 80% of the cultural spring of Tamil Nadu itself is based largely on the saivite and alvar saints compositions for both the Vedic and Puranic matrices in Hinduism. The 20% "local" distinction is found in every region....and there is nothing really nationalistically attributed to it, especially in todays politics.
That doesn't stop people from trying to create and perpetuate new divisions from foreign sources/ideologies.
@Gibbs for one can tell you the Vatican's role in the Tamil separatist movement that existed in Sri Lanka. But overall in South India, people are quite wary and attuned to these mischievous forces increasingly, especially the more they try to create something out of nothing....like some seem to have gone full on here to portray....and even calling for the same thing in Pakistan and China (which does mark a departure from the earlier presence of this argument for India only).