nope, all guesses wrong.
the CLICK is the solenoid actuating, but not energizing the starter. this is caused by the contacts in the solenoid being worn. you will need to pull the starter, and either replace the solenoid, or rotating the two main bolt heads for new contact with the contactor ring.
most just replace the starter.

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John HAUL AWAY, OR CRUSHED CARS!!! HELP ME keep the cars out of the crusher! A/C Thread
"as I ride with my a/c on... I have fond memories of sweaty oily saturdays and spewing R12 into the air. THANKS for all you do!

My drivers:
1987 190D 2.5Turbo
1987 560SL convertible
1987 190D 2.5-5SPEED!!!

1987 300TD
2005 Dodge Sprinter 2500 158"WB
1994GMC 2500 6.5Turbo truck... I had to put the ladder somewhere!