Intermittent starting problem on 4-runner

I have a similar problem as the tundra person, although there is no rhyme or reason behind it starting or not starting. When it won’t, or when it has trouble, it goes “dit dit dit dit dit” and then catches, or sometimes not and must be jumped. I had the battery and the alternator tested and both were fine. What is the solenoid and what should I do?

Starter solenoid (which has the positive battery cable attached)is what supplies the power to the starter Bendix gear which engages the flywheel to turn the engine over.

If the contacts in the solenoid OR the battery cable connection is faulty, it won’t engage.