Brake light wiring

[psoucy]

I bought a set of led tail lights and the tail light sockets were in rough shape on my 70 K10 so I bought a set of aftermarket sockets. Couldn’t get the plug to engage so I took out the socket, clipped the plug and just going to hardwire. Now I have 3 wires, one brake, one tail light/signal and one ground. The brake light I believe works through the signal light wire so do I twist the brake and tail light wires together to connect to the one wire going to that side. There is a wire in the Painless harness for a 3rd brake light I could use but I’d rather not have to run a separate wire all the way back. Thanks in advance for any help with this.