did the blinker still work when the brake lights didn't?
the reason the blinkers don't blink now when the brakes are on is that you have bypassed the blinker with your "just run a wire" setup, that's normal behavior
the blinkers work by interrupting the power to the brake lights, so the problem may be the switch itself, but more likely a connection from the brake light switch to the blinker assy
Bill