The plate lamp is fed by the same circuit as the rear brake light, so if one works the other one is likely bad. Either the bulb is out, or a wire is loose. If it is LED, then maybe the wires are backwards. It should be fed by a blue with red strip wire (Hot) and a black wire (Ground).
I was leaning towards a bad ground, but it may be the backup fuse (#5). Easiest place to start is to check all the fuses behind the left side mid (clutch lever side).