I had an odd starter problem a couple of months ago. Got to where it was intermittent. Would start up fine several times, then nothing. For a while it seemed like fiddling with the signal would fix it, but it finally got to where that didn't even work. Not even a click out of it. So I pulled the starter and found something really interesting...
The wire that comes up through the center of the signal wire terminal was loose, sticking straight up and not touching the terminal. ALL of the solder was gone, apparently melted off. I bent the wire back into place, and made sure to flow on a decent amount of solder and put the starter back on. Has been working great for 6 months now.