2003 Ford Explorer Sport rear turn signal acting up

There is no flasher relay , all done electronically by the smart junction box (computer )
The smart junction box (SJB) monitors the multifunction switch position by sending multiple voltage reference signals to the multifunction switch. When the multifunction switch is in the LH or RH TURN positions, or the hazard lamp switch is engaged, that input signal is routed to ground.
When the SJB receives an input from the multifunction switch indicating a request for a turn signal or hazard lamps, the SJB then supplies voltage to the appropriate turn lamps.

Your best bet would be to take it to a qualified repair shop or dealer .
Do you know what DTC'S are ?
Smart Junction Box (SJB) Diagnostic Trouble Code (DTC) Chart DTC Description Action B1499 Lamp Turn Signal Left Circuit Failure Go To Pinpoint Test M . B1502 Lamp Turn Signal Left Circuit Short to Ground Go To Pinpoint Test M . B1503 Lamp Turn Signal Right Circuit Failure Go To Pinpoint Test M . B1506 Lamp Turn Signal Right Circuit Short to Ground Go To Pinpoint Test M . B2048 Left Rear Turn Lamp Circuit Short to Ground For Mountaineer, Go To Pinpoint Test M .
For Explorer or Explorer Sport Trac, REFER to Stoplamps in this section. B2049 Left Rear Turn Lamp Circuit Open For Mountaineer, Go To Pinpoint Test M .
For Explorer or Explorer Sport Trac, REFER to Stoplamps in this section. B2050 Right Rear Turn Lamp Circuit Short to Ground For Mountaineer, Go To Pinpoint Test M .
For Explorer or Explorer Sport Trac, REFER to Stoplamps in this section. B2051 Right Rear Turn Lamp Circuit Open For Mountaineer, Go To Pinpoint Test M .
For Explorer or Explorer Sport Trac, REFER to Stoplamps in this section. B2071 Hazard Switch Signal Short to Ground If the hazard lamps are inoperative, Go To Pinpoint Test N .
If the hazard lamps are always on, Go To Pinpoint Test O . B2281 Right Turn Switch Short to Ground Go To Pinpoint Test L . B2282 Left Turn Switch Short to Ground Go To Pinpoint Test L . All other DTCs - REFER to Section 419-10 .

2000 ford explorer combination wiper turn signal high beam switch...

Sounds like the wheel bearing inside the hub is going bad.

More than likely the "multi-function" switch is bad. It is actually the turn signal, headlamp lever which is affixed to the switch which is located in the steering column.

Replace right rear tail light bulb holder. Bad ground.

Check the bulbs if the bulbs are good suspect the panel that the bulbs go into. Which are also called the sockets you may have to replace the sockets this is not an uncommon problem.

I have a 2003 chevy silverado and the passenger side power window does not lock or the window wont go down.

The ford explorer sport track. Will have a short either at the plug of the multi-function switch or 6 inches down where the column bends the wires during tilt.

Rear lights are double filament bulbs one side for the lights other side for the brake/turn signals so it still may be a bulb. Do u have a test light or volt meter you can check to make sure u have power there when brakes or turn signals are activated. Or just try another bulb.

i think you can do it, heck your half way there. seams like you know what your looking at, go for it. trial and error best teacher. OLD SCHOOL.