OH HELL I'm AFU here!!! Somehow I was thinking you have a later model car. (4x switch in the column)
OK, man!!!
Here's how the dash mount 4x flashers work.
First, your column signal switch outputs all 4 corners, left, right, front rear, on FOUR separate lines.
BUT the TS switch WHEN CENTERED connects both the REAR conductors together so that both brake lights work. That is, when you mash the brakes, the TS switch routes power to both rear bulbs when the switch is centered.
So at the instant that you flip your switch for 4x, you should have the switch centered, and you have essentially (electrically) THREE wires
Now the 4x switch has 4 terminals
When off, NONE of the terminals are interconnected
When on, ALL of them are connected together.
The switch receives power from the 4x flasher on one terminal
The other three go to
left front
right front
the brake lights power going INTO the turn signal switch
So now, when that switch is on, the flasher feeds power to all three of the above.
MAKE CERTAIN that your brake lights are properly working. If so, and IF only some of the lamps are lighting, then it's either bad connections to the 4x flasher switch, or a bad 4x switch