Ok, so as per instructions from ncranchero I checked the wiring to the brake switch, and the brake switch itself. The switch works fine, but there is no power getting to it.
Further, I went ahead and bypassed the normal wiring and provided 12v to the brake switch directly with another wire running from the brake switch to the green wire.
My thinking was that if the only problem was that the brake switch was not getting power, then providing that power should cause the brake lights to work when the brake peddle is depressed. Right?
This however, this did not work. None of the brake lights function.
Also interestingly enough, it's clear someone has been under that dash and monkeying around because pulling Fuse 1 doesn't cause the taillights to turn off...