Hi!
I've seen so many 'toos with problems related to people petting/stroking them like dogs or cats. I'm not going to tell you not to pet your 'too but I would suggest limiting any stroking and also get to know what your bird can handle and what may be too overly stimulating. The hardest part of not stroking a 'too is stopping the human

These guys are 'toos....they're busy with things and they will find other activities if given the chance. Instead of stroking sessions maybe consider ways to enrich your relationship even more by taking strolls around the house, look out windows together, play games, clicker training...birds love clicker training.....let them help out with chores....they're real good at helping you fold laundry...as long as you want to continue folding it over and over and over again ;-0
Down time....best spent getting some head scritches while sitting on your lap or knee. An occasional hug, occasional stroke....
Problems I have seen associated to stroking that stimulates a 'too is overbonding, screaming, biting, plucking, excessive egg laying and in the case mostly associated with U2's...cloaca prolapse.
Shauna