Brake/tail light issue

Either you have a defective light or you connected the light's wires to the bike incorrectly.

Ah, that changes things. If the original wiring has an issue then you needed to fix that first. I don't remember where the fuses are for the lights (under the ride side cover, I think) but others should be along to provide specifics. If the fuses are good you need to look at the wires' connections for corrosion and to make sure they are actually connected. If all are connected, you need to check the wires themselves for shorts or breaks. Easier said than done, but start with the easiest first and work towards the most difficult.