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Neither the gun nor the [towing] vehicle can fire during the player turn in which it is being hooked up, moved or unhooked.and
A vehicle my unload an AT gun at the beginning of any Movement Phase it has all of its MP for the phase remaining. It must then move out of the hex...
So, not only is having all MPs left for the halftrack a prerequisite for unhooking, the ht then must leave the hex. And, having been unhooked, 48.6 kicks in: in the player turn of unhooking it can't be fired.