sounds like you've inherited some creative wiring!
Is anything else a lil wierd? Do the turn signals and tail lights work normally or are they screwed up as well, what about the hazard flashers?

On 69's, the backup light switch (and neutral safety switch) are on the lower steering com, up under the dash, and near where the brakelight switch is. The wire supplying power to the backup lights is pink, and the wire going from the switch to the lights is light green.

Because of the directionals, the "brake lights" are wired separately, from the steering column. pass side is dark green, drivers side is yellow.

On the brake light switch, power in is red, signal out is white. Signal out goes into the steering column.

Note these wire colors are from the 68 diagrams, but I believe 69 to use the same color wires.

 

Maybe they but the bulb sockets in the wrong holes?

 

I ran across a similar problem where a buddy's dash lights would come on when hitting the brakes. Turned out to be the wrong bulb (1156/1157?) crammed into one of the tail light sockets.

I'd start at the sockets and verify that voltage is getting to the backup sockets with all the bulbs out . Check tail and stop the same way.

Let us know what you find and we'll back track from there.