I would first suspect a bad ground..
blown bulbe maybe,or bad light switch.
it works when the lights are off but it is slow
the flasher could be bad,turn on other side blinker listen for the clicking should be under dash on pass side,if it blinks normal on one side and slow on other,its bad.all you have to do to get to it id drop down glove box,their is 2 tabs at top when open push them up let glove box drop all the way down,you will see a few relays turn on key switch then the turn signal feel which one is bleanking,turn key off pull out replace.
Looking for a Used Mustang in your area?
CarGurus has 41,500 nationwide Mustang listings starting at $1,488.
Search Ford Mustang Questions
Ford Mustang Experts