Thanks, MichaelFregoe.

This may just be my problem too.
My car usually takes 4 or 5 turns of the ignition key before the starter motor starts to crank.

I jumpered the starter cutout relay following your instructions and it started right up, 1st attempt.

Strangely, I have put the connector back on the relay and tried to start it about 10 times and it always started right up. Does the jump wire "reset" anything ??

 

Any chance the cutout relay gets corroded on some cars?

My lack of solenoid response is intermittant; and I can usually get it to engage if I flick the key back and forth quickly, like getting some relay part to move,
when whack doesnt work,
whack whack whack seems to usually get something moving.

The intermittant part never intermits when it is at the mechanics.

 

It finally got bad enough that the starter did not respond while the car was at the mechanics! They have been checking voltages and replacing one chaffed wire and ... and...
They gave it back to test drive, and it worked ok again for a day, then went back to being intermittant.
It has also begun to hesitate and surge at low rpm light acceleration. I don't know if that is related, or just happened to occur at the same time.