The leaders of the TTP who are mercenaries. This is nothing new, such
asymmetrical warfare has been seen many times before. Again Pak made a mistake joining the immoral war even allowing drone strikes on their own people but those days are long gone now. Pak army now has almost wiped them out. Its a lot easier to do this when their is no foriegn support.
If the leaders of TTP are mercenaries, meaning they're primarily motivated on monetary terms rather than ideologically, wouldn't it make sense for Pakistan to simply pay them off more than what India does to buy their loyalty? Besides, wouldn't it make more sense for India to buy mercenaries in Pakistan's side of Kashmir to foment trouble there and give headaches to Pakistan in their side of the Kashmir just like India has its own issues in the Kashmir valley, rather than going all the way to Afghanistan to cause trouble in KPK. Or the ISI could pay off similar mercenaries to cause trouble in India, there's no shortage of people who want money in the world.
The simple fact is, a movement headed by mercenaries will never be sustained and get popular support unless there's a prevailing sentiment in the society. Otherwise Pakistan could have paid off similar "mercenaries" in Punjab or even elsewhere to cause trouble for the Indian state. Most of the fighters in the current Afghan Taliban were borne out of brainwashing of the Afghan refugees (and fighters from Pakistan too) in the hundreds of madrassas set up in Waziristan by the likes of Zia to deal with the problem posed by a nationalist Afghanistan from Pakistan's pov.
When you brainwash thousands of young impressionable men that any form of nationalism or democratic government is a sin and that muslim societies must always be governed by shariah rules, so as to have a favourable regime in Afghanistan [from Pakistan's pov, an islamist regime in Afghanistan is always better than a (ethno)nationalist one there], then think from the pov of a person who grew up in such an environment. For him, he wouldn't find difference between Afghanistan or Pakistan and particularly for a person who was born and brought up in Waziristan and grew up in such a radicalising environment, he would of course want shariah in his region too just like his Afghan mates in the Afghan Taliban who fight for shariah in Afghanistan.
I know the TTP and Afghan Taliban are different entities, but the TTP definitely seeks inspiration from the ideology of Al-Qaeda or the Afghan Taliban. The ones who did the siege of the Lal masjid in Islamabad were also closely allied with Al Qaeda and inspired by Bin Laden. You can't brainwash thousands of fighters and expect them to be islamist in Afghanistan and defy their democratic government there but suddenly obey the laws of the land and democracy in Pakistan. It doesn't work like that. The TTP deals in a lot of suicide attacks against the Pakistani military and even the minorities like shia or the hazara population and it's not easy to find mercenaries who blow themselves up for a cause unless they're ideologically motivated rather than monetarily motivated like you seem to imply.
I cant think of any other reason why India is desperate to remain in Afghanistan. Can you think of any? Please dont tell me they care. $3 billion would have done a lot of caring for the hundreds of millions of poor in India. Do you support Indian boots in Afghanistan and do you think they could do what Nato couldnt?
I'm not under any illusions and believe India is the most noble and therefore supporting the Afghan government. Countries ally with each other and support each other for mutual interests, that's why the Soviet Union allied with India in the past and that's why China allies with Pakistan currently. From an Indian pov, a stable Afghanistan is in its interests because then it would provide them a route through Iran and Afghanistan to access central asia, as their relations with Pakistan are strained due to obvious reasons. Besides, a stable Afghanistan is in India's best interests for the same reason that a stable Pakistan is in China's interests - that they would serve as counterweights for their respective rivals in the region (Pakistan in the case of India and India in the case of China).
And no, I would never support the presence of Indian foot soldiers in Afghanistan. That would be a debacle and would not happen in a million years anyway. That said, apart from all the realpolitik talk, I personally think the Afghan government is better suited for the future of the Afghan people than any form of Taliban. The Afghans largely seem to think the same and it's always better to support something what the people of a region want than what they oppose. I don't think India should provide foot soldiers, nor do I think the Afghan government will ask for it, but I do think India needs to support Afghanistan in whatever way it can, whether by building infrastructure or dams or hospitals or even providing non personnel military support in the form of arms and ammunition.
The Taliban who have just hammered the American's will be waiting with flowers and ladu's!!
