After what Keith mentioned above, it got me thinking that I haven't opened up my FXX in quite awhile so I didn't remember if there was anything different about the brass rails for the lights.
So after opening my car, it does appear as the pic below indicates, that SCX was suppose to insulate the rails on these cars. This is actually a "factory" tape job which explains why I never had any issues.
So if your car never came like this, you need to do what is shown above.
Also, here is a pic showing the chassis and body side by side. If you notice, the chance for a short can occur where the motor capacitor (orange part soldered between the motor leads) is located which would explain why the lights only worked when the light circuit touched the motor pads.
So once you tape up those light circuits, you should be fine from this point forward. Obviously, SCX should have taped in the first place.
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I just realized from reading the original post that the car in question was "used". Thus, I don't want to imply that SCX missed the spot if there is a chance that the previous owner of the car inadvertently removed the tape. Although, I wouldn't be surprised if a small number of these cars could have came with no insulating tape.