I had a similar problem with a '93 Caprice. I did all the usual troubleshooting, but everything checked out.
You know how they wipe dielectric grease on the bulb bases to prevent corrosion? Well, there was PLENTY of grease in the sockets, but it had become semi-hard and was preventing the bulb from seating fully against the contacts! (Removing and inserting bulbs would push the gunk around just enough for it to interfere.)
I was able to scrape out much of the crud with a small screwdriver, then about half a can of contact cleaner spray and various swabs to get the rest. Never had another problem with the lights.