It's a manual tranny. OK, that means it's not a defective neutral safety switch because it's used only on automatics.

It clicks.

The clicking is probably the solenoid pulling in.

This sounds very much like an intermittent starter, although I thought you said the starter had been replaced. Are you sure?

If the battery is charged and the voltage remains up, then it's probably not the battery. But it could be a bad ground connection or bad power connection at the solenoid. It could also be a bad (or loose) connection of the heavy conductor 'tween starter motor and solenoid, which is secured at the solenoid with a heavy screw.

I'd wager my first cold on on a bad solenoid.

I'd wager my second cold one on a bad starter motor.

I'd wager my third cold one on a bad connection 'tween starter 'n solenoid.

I'd wager my fourth cold one on a bad power connection at the solenoid (red wire).

I'd wager my fifth cold one on a bad ground, perhaps a loose starter bolt (seen it happen...).

I'll just drink the sixth cold one because by now you don't want me near your car.
--
Don Foster (near Cape Cod, MA)