My rear turn signals are not working. front turn signals work rear parking lights work brake lights work

Are you familiar with vehicle electronics ? BCM - body control module ? Parking light's an brake light's have nothing to do with the turn signals .
Turn Signal Lamps
The body control module (BCM) is responsible for controlling the turn signals and hazard lamps. When the turn signal switch is placed in either the left turn or right turn position, the BCM receives a signal from the turn signal switch. The BCM then sends an on-off voltage signal to either the left or right turn signals and their instrument panel cluster (IPC) indicator. When the hazard switch is pressed, the BCM receives a signal from the hazard switch. The BCM then will send an on-off voltage signal to all the turn signal lamps. All the turn signal lamps will flash including both IPC turn signal indicators.
Your best bet would be to have diagnosed at a qualified repair shop .

In the diagram for rear lamp, the top wires are voltage, the bottom black wire is ground. The brown wire on either side should be tail lamps, goes hot when you turn on the headlamp switch. The other top wire on either should be for turn signal. With everything turned on, is there voltage on that wire?
Because the front works and the rear don't, possible wiring circuit problem? The voltage for turn signals comes from bcm. The bcm knows when you turn on turn signal switch, either side, then the bcm sends voltage to turn signal lamp at the rear and front.