In 1968 my parents bought a new Olds Cutlass S. You could shut it off and it would sit there chugging away for up to a half minute. I wondered what would have caused that. I kind of remember my father finding out that it had the wrong spark plugs. And what would the engine most likely have been.
I had a 68 vista cruiser, it had the “400 turnpike cruising package” they say it was a higher compression 400cid. Maybe you could research that?
It's called dieseling and it is caused by a throttle that doesn't close sufficiently (too high an idle in some cases) and a latent heat source in the cylinders. (For your dad's Cutlass, the wrong spark plugs.) Dieseling was a big problem for early emission control cars. One way to (crutch) solve the problem was to shut them off in gear. GM's cure was an idle speed solenoid that completely closed the throttle blades when you shut off the engine so no air/fuel good get by to be ignited.
Another brain child idea GM had was to engage the A/C compressor to load the engine to get it to stop running. Sent from my iPhone using The H.A.M.B. mobile app
The Turnpike cruiser package was not a higher compression package. It was a 400 2 barrel with a rear gear ratio around 2:56. Was set up for gas mileage.