No brake light or hazard warning flashers in rear

Doesn't have a turn signal flasher , use's lighting control module .
Turn Signal and Hazard Lamps The turn signal system consists of:

• turn signal miniature bulbs (13465).
• turn signal indicators in the instrument cluster (10849).
• lighting control module.
• multi-function switch (13K359).
• circuit wiring and circuit protection.

Power is supplied to the lighting control module through instrument panel Fuse 6 (10A). This fuse is hot in START or RUN. The lighting control module is connected to the turn signal switch portion of the multi-function switch. Ground is provided to the lighting control module and the turn signal miniature bulbs through Circuit 57 (BK).
Turn signal functions are performed by double filament bulbs in lamp assemblies located next to the headlamps. The turn/hazard function uses the second filament of the appropriate bulb(s).

• With the multi-function switch in the right turn position, power is supplied to the RH front and rear turn signal miniature bulbs and the right turn indicator in the instrument cluster.
• With the multi-function switch in the left turn position, power is supplied to the LH front and rear turn signal miniature bulbs and the left turn indicator in the instrument cluster.

What fuse are you pulling ?

Hazard Lamps
The hazard warning switch is part of the turn signal switch. The turn signal switch receives battery voltage at all times through the HAZARD SWITCH Fuse. When the hazard switch is placed in the HAZARD position, battery voltage is applied to the hazard lamp/turn signal lamp flasher. The hazard lamp/turn signal lamp flasher sends a turn signal flasher signal to the turn signal switch. The turn signal switch provides all of the turn lamps and turn indicators with the turn signal flasher signal, simultaneously flashing them on and off.

Turn Signal Lamps
The front turn signal lamps are made up of the front park/turn signal lamps and rear turn signal lamps. The front turn signal lamps flash with the rear turn signal lamps when a turn is initiated using the turn signal/multifunction lever. The turn signals will operate only with the ignition switch in the RUN position and will not operate during hazard flasher operation.
When the ignition is turned to the RUN position, battery voltage is supplied to the TURN SIGNAL Fuse. Battery voltage is then applied through the turn signal fuse circuit to the turn signal switch. When the turn signal switch is placed in the LH or RH position, voltage is supplied to the hazard lamp/turn signal lamp flasher. The hazard lamp/turn signal lamp flasher supplies a turn signal flasher signal to the turn signal switch. With the turn signal switch in the LH or RH position the corresponding turn signal indicator, rear turn signal, and front turn signal receive the turn signal switch signal and will flash. The front turn signals receive the turn signal switch signal from the turn signal switch via the BCM. The turn lamps are permanently grounded.

Replace the turn signal switch. Refer to Multifunction, Turn Signal, and Hazard Switch Replacement - On Vehicle in Steering Wheel and Column - Tilt.

Brake lights /rear hazard lights not working - Ford Truck ...

www.ford-trucks.com > ... > 1967 - 1972 F-100 & Larger F-Series Trucks
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YOU MIGHT HAVE A BURNT OUT RELAY IN FUSE COMPART UNDER YOU CARS HOOD CHECK THAT OUT THRU YOUR CARS MANUAL,IT WILL SHOW YOU WHICH RELAY IT IS?

did you change the flasher relay ? it controls the flashers and the hazard

Your turn signal flasher is separate from the hazard flasher. Replace the turn flasher.

Both the turn signal flasher and the hazard warning flasher are mounted on the fuse panel on the truck. To gain access to the fuse panel, remove the cover from the lower edge of the instrument panel below the steering column. First remove the two fasteners from the lower edge of the cover. Then pull the cover downward until the spring clips disengage from the instrument panel.
The turn signal flasher unit is mounted on the front of the fuse panel, and the hazard warning flasher is mounted on the rear of the fuse panel.

Hazard light switch... They all intermingle in operation.
My ex wifes 96TC was doing the same thing... I could OCCASIONALLY get the hazards to work by turning the hazard switch on/off like 10 times in a row and suddenly it would fix... finally bought a new switch

Suggest you change hazard flasher 'can' first, then go to the hazard switch. I'm betting it's the flasher can.

There are two thermal flashers one for the Hazard Warning Lights and one for the Turn signal lights. It could be the flasher for the turn signals.