Interesting...maybe some swaps were done. If there is a vacuum hose to the changeover switch above the go pedal, plug it and see what happens re: shutting the engine down. It doesn't take much of a leak to stop the vacuum engine shut-off.

Check the inline vacuum filter near the firewall, engine side (looks like an early VW Bug fuel filter) for cleanliness and the that the port off of the brake booster vacuum hose to the vacuum system is not restricted.

How well do the trunk and door locks work and how crisp is the shut-off when the AC is in off mode?

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