Starter problem 84 GL1200A

[aspengold]

I am having an intermittent starting problem. When I press the starter button, 9 times out of 10, I get a click and that's all. I have had the battery tested, replaced the clutch switch, checked all the wires for problems and corrected a few, I have checked the ground wireing and it seems to be OK, the solenoid has the blade type fuse. If I pull the side cover and jump across the battery and starter cables the bike will start up without a problem. On occasion if I press the starter button and hold it in for a few seconds the bike will start. This does not work every time. Do you think replacing the solenoid might correct this problem?

Bob