Hazards blow fuse, brake lights don't work...

Hmmm... you replaced the "electronic flasher behind dash on rear of central junction box", right? I would check the LT BLU wire and the WHT/RED wire (coming out of that flasher going to the multi-function switch) for damage and shorting to ground. Shorting to ground is why the fuse blows.

Your parking lights work fine so that eliminates the brown wire. You said you have rear side markers, right? So those grounds are fine.

I would also check your main wiring harness connection on the left side of the dash and check all the dark green wires. Should be five. One goes to your third brake light and that works but two others power your rear brake lights.

Troubleshooing blown Fuse F2.13 w hazards

Please confirm a few details. Please answer all of the questions and perform all of the tests. This is necessary to narrow down where to look for a problem.

Double check fuse F2.18, F2.13, F2.33, F2.41, F2.35. Pull each fuse and test with an Ohm meter. Report ALL fuses that are blown.

F1=BJB=Battery Junction Box-located left engine bay
F2=CJB=Central Junction Box-located driver's kick panel.

Confirm that the battery terminals are clean and tight. Clean all corrosion. Check the grounds around the battery and radiator core support.

Confirm if the turn signals work from the FRONT and REAR. Actually check and note if correct brightness.

The 3rd brake light does NOT come on when the trunk is opened. That is simply the trunk light shinning through the lens. Confirm if the 3rd brake light comes on when the brake pedal is pressed. This detail is important because the 3rd brake light does NOT pass through the multi-function switch.

Confirm that the parking lights work. Check the front and rears. Confirm the brightness of the bulbs.

Confirm that the correct blubs have been used. IE, no bright aftermarket bulbs. Check all bulb sockets for moisture and corrosion (front and rear. Esp the rears).

Check ground G204 located to the left of the center console. This ground is shared by the cluster, GEM, AC/heater blower, and radio. Has there been any recent radio work?

Check ground G400 in the left hand side of the trunk (near FPDM). Will be necessary to remove the trunk liner. Measure the resistance from the stop light BK wire back to battery negative. Post. If there is a break in ground G400, this would stop the brake lights from working.

Check ground G102 and G103 located around the front radiator core support(front turn signal grounds).

The above tests will help decide where to look next.

EDIT: I have been thinking about this and there may be a simpler explanation. The OP stated that the brake lights do not work. It's assumed that fuse F2.33 and F2.41 is good. This should be doubled checked.

Pull fuse F2.41 and verify there is power in the fuse slot when the brake pedal is pushed.

Seems likely to me that there is a fault in the brake circuit and this is also causing fuse F2.13 to blow when the hazards are used.