'86 900 starter problem/questions

I've got an '86 Saab 900, normally aspirated. In the last week,

3 times now, the starter has failed to turn over the engine when I turn the key. First time, I let it sit for a few minutes and tried again, and it fired right up. Second time, I was able to roll-start it (I parked on a hill) and it started right up, no hesitation at all. So, I don't think it's a battery issue. Third time is this morning and it's resting comfortably in front of the garage, waiting for me to come home.

So, I don't think it's a battery issue, or it wouldn't have push-started so easily, right? or, not? I'm getting the relay "click" and the fuel pump does come on for the second or so, so I think that means my ignition switch is OK, yes?

What I think this leaves as a possibility is the solenoid on the starter itself. Does this sound logical? If so, is the H-engine starter the same as the B-engine starter? Those, I have a few of, the H-engine type of course I don't.

Thanks for any suggestions, Dave Hinz