sounds like a short, the short causes the voltage to drop to the solenoid so much that it clicks off, when it clicks off the voltage comes back up cause there is no load, allowing it to re-energize, (click again).
what if you jump right to the starter? this will eliminate the solenoid. be careful, if the starter is shorted it will melt stuff
2000 Vulcan Drifter 800
Roadhouse classic 2 > 1 exhaust
Okie Smokie intake config
52K miles or so, always going up
Painted flat black winter '12