Ah, truly "the enemy of my enemy is my friend" holds true. I googled the state and wow, they're like just half of the population in the state and they were already acting like this (still beats being a nuisance at just 5% like, ahem...).
I could see why Pakistan would want this as a separate country, they probably like the possibility of it eventually joining the larger Punjab region in Pakistan. I there a larger Punjabi independence movement there? The Punjabis seem to be a bit like the Kurds, an ethnic group split between two countries. Although in this case there is also some religious difference between the two Punjabs.
The Khalistan movement never enjoyed majority backing among the Sikhs in India. Most of the army officers who put down this rebellion during the 1990s were religious Sikhs themselves. And also, Sikhs are less than 50% of the ethnic Punjabis in India, although in the state of Punjab they may be a majority. Hindu Punjabis are more spread out, with sizable populations in Rajasthan, Delhi, and Haryana.