I finally fixed mine!
Here's some back story: I've had the clicky starter issue for years, and it had been getting really bad in recent weeks. I had assembled several good starters from my parts bin, and even put a new solenoid in a few months ago that didn't help either. I could hear the solenoid click, but the starter motor wouldn't turn, so I couldn't wrap my head around the possibility that the problem was between the ignition switch and the starter solenoid. I could hear the solenoid click, so I figured it must be doing it's part. I had new battery cables, ground straps, a good set of brushes, strong battery. Nothing helped, the problem just kept getting worse.
About four days ago I put the car on the lift, and noticed that it cranked every time I jumpered the starter with a screwdriver; it almost never worked with the key at that point. As a test, I installed a temporary relay right by the starter as sort of an "electronic screwdriver". So far it has never missed a single start! YAY!!!. If there's a relay under the dash, I believe it to be the culprit. The Ignition switch, (or original relay whichever the case may be) sends enough current to trigger my temporary relay every time, but apparently not enough to trigger the starter properly.
All it took was this simple mod like Yam Yam said: