2.5 year old pulling hair out at night

My son always played with my hair when he was breastfeeding and bottle feeding. Since the age of 2 (so for the lady 6 months or so) when bottle feeding stopped he has been playing with his hair for nearly two hours at night before falling asleep, despite saying and acting very tired before going to bed.

It started with twiddling the hair but has now turned into pulling it out. So much so that when I run my hand across the sheets there are numerous strands, way more than a handful and I sometimes find clumps from the twiddling on the floor. He is pulling around the crown and therefore the hair looks like that a male baldness with long hair at front, back and sides, but bald on top.

The first thing he says to us when we go in in the morning is I pulled out my hair or I didn’t pull out my hair. The latter is more worrying as we know he has, so he seems to be lying, but we thought he was too young to understand lying, but clearly not.

We’ve tried not to make an issue of it and don’t tell him to stop or ask why he is doing it. We have asked him how he feels when he does it, but he just says don’t know. He has cuddly toys in bed and we recently got him a resort wooden worm to play with, but nothing distracts him from the hair pulling. He doesn’t do it at all in the day, only at bedtime.

Can anyone offer any advice on how we should deal with this? Would cutting the hair short help? I’m worried this will really distress him.