Check your grounds as mentioned above. Then let us know. If you see a faint light and the flasher is new, then it has to be a ground problem, whether that ground problem is at the socket, turn signal switch, or somewhere else in between.
If your wires are hacked, then that could be the problem too. As you mentioned, you may want to look into re-wiring if you have the means to do it. Wiring poses a lot of problems loke this if it's not in good shape.
To adrdess this issue, start from the sockets and work your way back to the switch. You can sse the wiring diagrams at the following site to trace the wires.
