Keeps wanting to go get hair cut

Maybe the attention feels good. Maybe it brings him comfort. I would say yes.

I wouldn't argue about when he had his last haircut. Maybe brush his hair and tell him how good it looks.

Possibly collude with the barber so the barber pretends to do something, although it would probably be appropriate to pay the barber for his time.

Could you try something like- they don’t have any appointments available til next week, or tell him you made an appointment and just keep pushing out, if his usual barber doesn’t usually do appointments could you tell him they now require appointments. Just some ideas. I hope you find a solution.