I switch my 2013 Cadillac reverse lights to LED's now they stay on why

Had the same problem on my vsport platinum. From what I could figure the LEDs take so little power that there was not enough load/draw to cause the control module to ever close the back-up circuit. My back-up lights would stay on dimly lit all the time. I lost use of the rear sunshade and self-dimming mirrors (both disengage when in reverse). The car battery would die after a few days if unattended. I changed the back-up lights back to super white incandescents, all problems magically fixed. The only other suggestion is to add LED ballasts to each reverse light, I was considering this but didn't try as I was happy enough with the replacement incandescents.

solved this same problem on an older car a few years ago. Took care of the same issue on my 2017 Cadillac XTS Luxury. SOLUTION: You have to put resistance on the bulb wires in the form of a resistor or one of the old bulbs you replaced. I used one of the old bulbs. Painted it black. Tied it into the line (bulb wires) running to the backup lights. Just tuck the resistor or bulb up on top of the inside of the bumper. No one will ever notice it and problem solved.

Same issue on my ‘14 LaCrosse Premium II. Just added a resistor to the light wiring by the housing and issues are gone.