The engine doesn't shift.
When driving a stick shift, you shift up as the engine begins to rev in each gear. You will downshift as the engine begins to slow.
you need a clutch that's all
The Ford C6 uses engine vaccum to sense the shift points. In a diesel engine setup there is a vaccum regulator to accomplish the same thing as in a gas engine.
no it doesn't.
nope the transmission shifts not the engine
if the engine isn't reved enough it will stall
Engine mounts could be loose or worn.
Your statement is a little inconclusive. Will the transmission shift when the engine is turned off, but not shift when the engine is running? If it is jammed and refusing to move even with the engine off, the problem will be inside the gearbox and usually related to the selector forks and or rods. If the the problem is there only when the engine is running the problem will be related to the clutch assembly, which is failing to disengage the gearbox from the engine
The shift solenoids are part of the valve body assembly. It is located on the transmission where it mates to the engine.
a manual shift "slapstick" option, letting you shift the transmission manually, but it still has safety features to keep you from damaging the engine or transmission
Engines work best in a certain range or RPMs (revolutions per minute). The time to shift is when you've moved outside that range. If the engine is spinning fast you change to a higher gear, if the engine is spinning too slow you shift to a lower gear.