” The headlights look normal to you driving the car. The car and light from the headlights appear frozen to everyone else ( this would actually happen if the car were entering a black hole, just before the event horizon - observers would see the car stalled at the EV, “never” actually entering)..”
Given that no light escapes the black hole, there will be no car seen entering.
However the light ‘stops’ coming from the car after entering the black hole thus it will disappear.
Before the event horizon, the car will NOT be seen normal as the light will be more and more red-shifted as it approaches the event horizon.
The red shift is another consequence of time. But the driver does not see any change.