click...click...click... DAMMIT!

Here's some additional on solenoids. I don't know if this holds true on mini-starters or not, but it's true of older 'wound field' Mopar and GM style starters.

The solenoid has TWO windings. A light duty "hold in" winding, and a heavy duty huge hi current "pull in" winding

What is important here is that the "pull in" winding is wired IN SERIES with the motor of the starter. What this means is, that if the starter proper has an electrical problem, the symptom will show up as "a bad solenoid." In this case it will not pull in.

In your case, the problem was likely bad contacts in the solenoid. In the GM solenoids, it used to be common to pull them apart and 'turn the washer' around (the contacts washer) to freshen up the contact for a bit longer.