OK
I ask about the tranny as the auto has a N safety switch that is in the circuit..
So,now I know we don't have that to contend with.
Here is a simple test.
You have either a bad starter contact ring in the ignition switch OR possible bad starter/brushes/solinoid [ or wiring in between]
If you take a test wire and jumper from terminal "G" at the time thermo switch [ this will be the short terminal] to Battery B+, the starter should turn [make sure you are in "N" for this jumper test]
Do it a few times , and if the stsrter cranks every time , you have verified its integrity.. concluding that you have a bad start/ign switch.
If no turn or not every time you jump, you have a problem down at the starter..
All that this test does is jumps past,and therefore eliminates , the ignition switch start feature/circuit
Bingo... let me/us know.........