With the pedal released, you should only see 12v on one side of the switch. The other side should be at ground.
If the hot side drops to 9v with the pedal depressed, there is a poor connection somewhere in the wiring (or possibly a bad ignition switch). I would check next at the 'green' terminal of the fuse block, to see if it also droops when the pedal is pressed. If not, the problem is in the green wire from the fuse block to the brake light switch; possibly in the bullet connector above the switch.
If the 'green' terminal on the fuse block does droop, then the problem is farther upstream. Next place I'd check in that case would be the 'white' terminal. And so on.
Now that you've dealt with why the supply voltage droops, what does the load side of the brake light switch do ? If it's the same as the supply side with the pedal depressed, then the switch is probably OK. If not, the switch is bad.