Brandon,
It sounds like you need to figure out where the wires are really supposed to go instead of just swapping them around. The bright headlamp is most likely caused by the tail lamp turning off first, before the headlamp.
Make sure the tail lamp bulb is really grounded. Then find the wire which is common to the headlamp power and connect that to the tail lamp filament (the thin one), The wire left over should be the brake light wire.
Ron