I've never heard of a HV driver and I've adjusted plenty of brightness pots in my time..

You can buy TV adjustment instruments from Jaycar etc - which are just plastic screwdrivers for adjusting pots and inductors.

Of course - on a standard chassis - You have a brightness pot, and you have a brightness pot on some EHTs.

not sure about a P2000..

The insulated shaft on a standard flat head should be fine - But the set from Jaycar and Dick Smith will do the job.