Solenoid mounted on starter body. Mine did this every few months, then all of a sudden did it every other start, then wouldn't crank at all. Don't get stranded, I had it happen twice when I didn't replace it.
I ended up taking my starter apart, seeing how bad the brushes and everything else was, and just said screw it and installed a new one, since my old one was a direct drive anyway, I got to upgrade to a Mitsubishi OSGR starter.
To test this, see if power is getting to the starter-mounted solenoid when you turn the key to the START position. If no power at solenoid, then the fender-mounted solenoid is bad (but you heard clicking so it's probably not that). If yes power, then test the output from the starter-mounted solenoid to the starter. If no power, it's the solenoid. If yes power, your starter is on its way out my friend.