There’s a switch on top of the intake that is one of only two possible causes of S4+ fans running after engine stop. The other is a similar temp switch on the auto gearbox.

The fans run based on coolant temp sensor in the radiator outlet side tank. They also use the system pressure in the HVAC system.

Running for a few minutes after engine stop is nothing to worry about. Much more than that deserves a look. Check the trans fluid and fluid level too, as that’s the only other tem that runs the fans after engine stop.

FWIW, I had to replace the intake switch a week or three after an engine bay clean and detail. Apparently the switch doesn’t like to get wet. Even in the dry desert climat above Los Angeles, the corrosion devils ate the switch guts.

Disconnect the brown ground round wire on the switch after checking the intake temp with the IR temp gun immediately after engine stop, while fans are/were running. The hood switch should stop the fans, so you may need to secure that for functional testing.