03 suburban reverse lights will not work
They are not in the same circuit. You have 2 different problems. Dome lights have a dome override button below and to the left of the headlight switch. See if that's pressed in. The reverse lights could be as simple as the bulbs are burned out. See if they are, if not test the bulb sockets and see if you have power to them while the gear selector is in reverse. Check fuses first.
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