Solenoid Test Results after starting over

[Longjack]

So here is what had happened in my recent tests trying to determine if I have a bad solenoid.

1.) Black meter probe left on battery ground post and red meter probe on large solenoid post attached to red cable from battery shows 12.88 volts.

2.) Black probe left on battery ground post and red meter probe then placed on large solenoid post which has cable gong to starter, then Key on and pressed pedal, hear the solenoid click, but NO voltage.

3.) With key off, pedal not pushed, take reading across the 2 large solenoid posts and have 12.88 volts. And of course, in this state, if I jump these 2 large solenoid posts, she starts.

Does this mean my solenoid is bad, i.e. has a short, or something?

Many thanks for any help.