S2, a further possibility with a car this age is having dirty starter motor to block/chassis earth terminal. Usually, but not always, at the chassis end.
Ditto for the battery to chassis/block earths.
Visual inspection is usually not sufficient to detect this.
Remove each of them to see if there is rust or other muck interfering with the current flow.
Clean all surfaces with fine wet and dry paper (100 to 180 grit), or dress them with a file to rough clean them first, if necessary.
Apply Vaseline to the mating surfaces of all components and reassemble tightly.
While you are up to your armpits in there, you may as well check the supply side connections as well ...
:iconwink:. Treat them likewise.
These terminations can look absolutely fine externally. It's only when you get them apart that the resistance causing problem becomes abundantly obvious.
If the starter motor solenoid is dodgy, and it's not a broken return spring, chances are that meticulously cleaning and lightly oiling the spirally turned engagement shaft will fix the problem. However, I'm not even sure that one can get at this part in modern cars ...