Has any after market type of electronics been installed recently (radio, CD changer, etc.) or even a trailer wiring adapter? If so, try disconnecting that and see if the problem persists. I had some similar type of issues with my '85 4Runner after swapping out a radio and used the PO's hacked up wiring to hook it up.

Otherwise, sounds like a ground issue, Toyota uses a lot of switch ground circuits for lights (a ground connection makes the light turn on). All fine an dandy until you lose a ground connection some place and then you'll find things like the parking/running lights find ground through the brake lamp filament. And that is fine and dandy until you apply the brakes (and that kills the ground path) and now all the lights go off. The fact that you see a voltage change at the parking lamp pin when the brakes are applied says this may be the case.