Early 70's Ford 302 Truck: Why does engine briefly speed up when turning key off?

Not a problem. I’m just curious why it happens. I turn the key off at idle, and the engine rpm subtly increases for about 1/2 a second or so, before it stops running. What could cause that?

Sounds like dieseling to me. The carb keeps dumping fuel into the cylinder, and the cylinder has carbon buildup or similar that causes hot spots with enough heat to ignite the fuel/air mix.

My old truck will sometimes just keep doing it until you slowly let the clutch out part way in gear to provide enough resistance to stop the motor before the next compression stroke on the dirty cylinder.

It may be dieseling and in fact it may be dieseling counter clockwise. A vacuum leak or excessive idle speed makes the problem worse. And for years Ford installed an anti-dieseling solenoid to the carburetor to virtually close the throttle when the ignition was turned off to prevent that problem.

https://www.google.com/search?q=anti+dieseling+solenoid+Motorcraft&client=firefox-b-1-ab&tbm=isch&source=iu&ictx=1&fir=BAkofvDyczSusM%3A%2CQgCtYB3pGxLomM%2C_&usg=__Hxcx1mIhsHLj-Nh03Sx78Gg32LU%3D&sa=X&ved=0ahUKEwiCh8W56_3aAhWJ61MKHfJ_C9sQ9QEISTAE#imgrc=chm7QtbeR2dZ4M:

Yes. It sounds to me like a malfunctioning or out of adjustment anti-dieseling solenoid.