[PeteLeathersac]

Do the headlights also shut down when the click thing happens?.
If so it sure sounds like connection, ground, wiring or solenoid problems more than the starter body itself?.
Using jumper cables from your own battery, create a direct ground by clamping the negative end to your starter itself and trying it again..
If no-go there, unhook the neg. cable and create direct positive to the starter connections using your battery jumper lead clamped to a long screwdriver if necessary to access the connections...being careful may involve slipping heater hose or something over the screwdriver shaft and/or getting the screwdriver end in first then having someone else hook up the live end?.

Good luck!.
[img]<<GRAEMLIN_URL>>/beers.gif[/img]
~ Pete