Hi @yingertony2 ,
I don’t know the answer but perhaps there may be a problem with the BCM (body control module) or perhaps the brake pedal switch or the wiring between the two.
Here’s an image from the wiring section of the 2013 Cruze repair manual showing the wiring (or part thereof) of the brake light circuit.
(click on image to enlarge for better viewing)
The red, blue and green arrows show the brake apply supply voltage (red), the brake apply sense signal (blue) and the low reference (green) wires between the brake pedal switch and the BCM.
The yellow arrow is the supply voltage to the Right rear stop lamp from the BCM.
The black arrow is the supply voltage to the left rear stop lamp from the BCM. .
The orange arrow is the supply voltage to the centre mount stop light from the BCM.
Can only suggest that you check the voltages from the BCM on the various leads to the brake switch and the stop lamps with the engine running and the engine off and with the brake pedal applied and normal to see if there is anything obviously different.
Hopefully this is a start and is of some help.