right turn signal working in front, not rear

[z6ne]

On my 91 318is, the right turn signal lights up in the front, but not the rear. The left signal works fine. When I push the lever right, the indicator on the gauge cluster blinks faster. Do I just need a new bulb in the rear or is it related to wiring?

[D J]

A new bulb would not hurt. if that does not work its most likely wiring

[AndrewBird]

When a bulb goes out, there is less resistance in the circuit which causes the flasher to flash faster. So yes, you need a new bulb.