hi Dave
normally it is the earth wire that causes the problem. Even though the plastic bulb holders look fine i would check inside the wiring black connector as the pins corrode inside there.
I would say try joining another wire to the earth and earthing this to the body of the car.
I would replace the holders anyway as a matter of course as they are not that expensive.
The last one of these i did in the end i had to cut out the black connector and use spade connectors to get it to work. Didnt look nice but that was on an old runabout.
Good luck
Paul