Okay Doug, This one has your name on it.
86 xj6 will start just fine most of the time. Every once in a while I will turn the key and the starter motor will not turn.
I open the bonnet and tap lightly on a row of relays located near the passenger wiper blade and it will start fine. Its probably a corroded connection, but I cleaned everything and even replaced a badly corroded fuse. I have been trying to isolate this problem for four months. Any ideas which component would be causing this?

 

Ill chime in here as I have had similar issues lately.

1. I had to adjust my inhibitor switch on the transmission. The small bolt was loose and the car would not start intermittently.

2. The red/white starter wire that goes to the silver relay on the firewall was one that I unplugged and jumped directly to the positive terminal on the batt. When the starter fired up every time I knew the starter was fine. I cleaned the terminal with sandpaper and put some bulb grease on it. So far no issues with starting the car at this point.

Try one or both of those to eliminate the inhibitor switch and starter as absolute issues.