Since I just put in a new slave starter solenoid I decided to see what the bad (intermittent starting, clicking, usually no ignition) one looked like. Here is a photo of the interior after I cut the metal tabs holding it together and pulled the cylinder out, the one that houses the actual magnet part and plunger. You can see one of the two copper contacts through which the starting current flows is pretty black. The magnet driving the plunger seemed to work OK, so I guess arcing did this. I wonder what would cause that - maybe the magnet coil is actually weak and it let the contact disc that touches those two contacts stutter up and down?