Originally Posted by Kornohalic
That is correct, and it will not stop spinning. I have to disconnect the battery.
Lets start at square one do you have a multimeter and know how to use it? If so you can disconnect the starter and work backwards from there to see where you are getting the voltage to turn it.
Unplug the two connectors going into the front of the solenoid and see if one or both of them have any voltage on them.
If you unplug both wires does the engine still turn over on its own?
This seems to be pointing at an ignition switch being bad
Here is a wiring diagram for the ignition this is for a 1967 just do a search for your 1965 and you can find the same images. I guess I have to stop reading to fast cause I just make up dates and see things that are not there.
67MustangEngineWiring.jpg Photo by mil1ion | Photobucket