[franken]

If there's no click from the solenoid it's a solenoid or wiring issue. The solenoid mechanically engages the starter drive (Bendix) and switches the starter motor.
I'd read and maybe reformat Rusty's post 7 to get after the issue.
For me I'd want to understand the issue mechanically and electrically in order to get on top of it. Of course, pulling and replacing the starter assembly is a pain, so many simply replace it.
Don't listen to any Ford solenoid nonsense. Adding more parts to a system you don't understand isn't an improvement.
As always poor grounds are a frequent issue. Ground the big cable to the block. I good spot is the front 50's motor mount hole.