When you say that the battery is in perfect health, does that mean that you load tested it against a carbon pile load?

It is not out of the question that you might need a starter. I have replaced the starter on my '91. Mine would start 9 of 10 times, but on the 10th time, just click. If you put it into gear and just bumped the flywheel a degree or two, so the starter got a slightly different engagement angle when it came out, it would crank vigorously and the car would start.

I was a little disappointed in my rebuilt Bosch starter. It makes a loud metallic churning sound when cranking the car. I considered sending it back but didn't want to go to that much work. It is a couple of years old, though, and still works fine. I have gotten used to the sound.

Before doing your starter, I suggest going to OSH or Sears and getting a 3/8" drive very shallow 6 point 18mm socket with a swivel joint built onto it. Works perfect for this job.