I can understand a gearshift so poorly designed that you might not know what gear you are in, but if you can’t tell whether the car is running or not, you probably shouldn’t be driving.
____________
My car has some sort of cool down system when I turn the car off. I could not tell whether it was running or not and had to bring it back to the dealer where they explained that ever though it doesn’t sound it, it is off.
That’s the damn electric fan due to front-wheel drive, and should still be prevalent but something must’ve changed. Rear wheel doesn’t need it as the fan always runs along with the engine crank.
Do you have a turbo- they build up so much heat that the cooler should keep running when you shut down so that the engine doesn’t cook itself from the residual heat.
I’ve always avoided turbos because of the heat issues.