2001 Ford Ranger right turn signal doesn't work when the braking

Turn signals are attached to the wheel, so likely a loose connector, or dirty connector from the wires that go from those into the harness. The brake pedal switch is close by so may join at that place. It is a case of getting under there with a flashlight, break the connections, check the contacts for corrosion or burning, and spray with electrical contact cleaner.

Stop Lamps
The brake pedal position sensor is used to sense the action of the driver application of the brake pedal. The body control module (BCM) provides a 5-volt reference voltage and low reference to the brake pedal position sensor. The position sensor provides an analog voltage signal back to the BCM that will increase as the brake pedal is applied. When the brake is applied, the BCM will then apply battery voltage to the left and right stop/turn signal lamp supply voltage circuits and the center high mounted stop lamp (CHMSL) supply voltage circuit illuminating the stop lamps. At the same time the BCM applies battery voltage through the signal circuit to the transmission control module (TCM) and the engine control module (ECM) indicating that the brakes are applied.
Ground for the stop lamps is supplied as follows:
• G402 provides ground for the left rear stop/tail/turn signal lamps
• G403 provides ground for the right rear stop/tail/turn signal lamps
• G301 provides ground for the CHMSL
The stop lamps on this vehicle will not illuminate unless the ignition is in the accessory, run, or crank positions. When the ignition is in the OFF position the stop lamps will not illuminate when the brake pedal is applied.
Battery voltage from the LT TRN/SIG and RT TRN/SIG fuses located in the rear fuse block is also used by the body control module (BCM) for stop lamp operation.

Turn Signal Lamps
Battery voltage supplied to the body control module (BCM) from the fuses listed below is used for turn signal and hazard lamp operation.
• LT TRN/SIG fuse for the left turn signals
• CTSY/RF TRN fuse for the right front turn signal
• RR TRN/SIG fuse for the right rear turn signal
When the turn signal switch is place in either the LEFT or RIGHT position, ground from G300 is applied through the turn signal switch signal circuit to the BCM indicating the turn signal request. In response to this signal, the BCM applies a pulsating voltage to the front and rear turn signal lamps supply voltage circuits cycling the lamps ON and OFF. At the same time the BCM sends a GMLAN serial data message to the instrument panel cluster (IPC) to cycle the appropriate turn signal indicator ON and OFF.
Ground for the turn signal lamps is supplied as follows:
• G104 provides ground for the left and right front turn signal lamps
• G402 provides ground for the left rear stop/tail/turn signal lamps
• G403 provides ground for the right rear stop/tail/turn signal lamps

Do you have a factory scan tool (tech2) ? Your best bet , take it to the dealer .

check the brake lamp/turn signal bulbs. sometimes in a dual filament bulb the filament will break and lay over on to the other, so when the turn signal is on and the brakes are applied, it just powers the circuit by-passing the flasher

Sounds like a short in the socket or a bad ground.
The parking light is one circuit and the brake turn signal is another.

try turning your lights on.....

The high mount stop light and the regular brake lights are actually on different circuits. The regular stop lights go through the turn signal switch which is known to go bad on older ford vehicles. Something to check into. Also be sure to check all the fuses.

it's in the turn signal switch behind the steering wheel.

It is as intended. If you check with everyone else, their car does exactly the same thing!!

Bad earth connection.Clean or replce wire.

there will be four wires going to your lights you will have to test each wire to see which wire is for the brake light and tap into that wire. on all ford rangers one bulb controls everything so you can't just hook it up thru your bulb so you will have to hookit up thru your wires. it's not that difficult but you will have to have a helping hand. and test till you find the one for the brakes only.