When you installed your ford explorer, did you also change the carvariations.meta file at all?
When i installed the LAPD ford explorer I had to add some lines to that file which correct the lights on it. Perhaps that file wasn't properly replaced when installing a new car.
I would, instead of keep trying to install new cars, to verify your game cache(if on steam version) and start new. This will not remove LSPDFR or any plugins. This will put every original file back that you changed using OPEN IV or whatever program you used.