Starter switch/relay lag

My 81 XJ 650 Maxim will often have a delay or no response when the starter button is engaged. If I keep pushing or trying it will eventually work (all but one time, when I had to bump start it ). I followed the procedure in an earlier forum and cleaned the contact in the button, with no improvement.
I have now noticed that when this occurs, the oil light comes on faintly. This tells me that the problem is not in the switch since it is making contact, but somewhere else. I plan to trace the wiring and check/clean all connections today, but any ideas/suggestions/tips would be greatly appreciated!
Thanks!
Shannon

 

If the oil light is dim then it suggests it is a power drop in the starting circuit to the ignition. I would check battery connections to the selonoid and the fuse box. My bet is on the fuse box.

 

Corrosion and possible bad connection thrown in for good measure, Max has your answer. You may find a little dielectric grease on your connections should help eliminate that issue.