There is no "plate" in relation to brake light wires.
There is a wire that branches and feeds both, the front and rear brake light switches. There is another wire that comes from both switches (and joins together), then feeds the brake light. There is no "plate" anywhere.
I think it has been hinted at here in this thread (I have helped in a couple other wirng threads recently, so am not sure if it was this one), but I am going to come right out and plainly ask you to do some testing, not guessing.
Look in front of the brake light housing. That would be under the "glove box" inside the tail fairing, behind the seat. You should see a flat, three-pin white plastic connector that feeds your tail light assembly. Note that there are three wires there, a black with white stripe (ground wire), brown (tail) and white (brake). Separate the connector. Use a piece of wire about two feet long (you do have some spare wire sitting around, don't you? If not, go get some), strip a bit of insulation off each end. Insert one end into the connector that is attached to the tail light, connect the other to a good ground (chassis, battery, whatever). Take another piece of wire about the same length, strip some insulation from both ends. Connect one end to a power source (fuse box, battery, whatever). Be careful that the other end does not touch any metal, or there WILL be fireworks. Touch the loose end to the brown wire in the tail light connector. You should see both bulbs light up, and be about equally bright. Now remove the wire from the brown wire and touch it to the white one, the brake light should come on brightly, the license light will not be on. If those simple tests do not work as described, you have problems with your tail light housing, the socket or the bulb.
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