Two speed rears are usually either electric or vacuum. The old Chevrolet rears were shifted by a vacuum cylinder. The vacuum cylinder was controlled by a mechanical cable to a vacuum valve. The cable was like a choke cable attached to the shifter which you would pull up or push down. In addition they had a small link between the vacuum valve and a two speed box on the speedometer cable. This allowed the speedometer to be adjusted for hi and low rear gearing. Some had a vacuum valve mounted under the dash that you would shift left to right for low to hi.
Most of the vintage you are talking about were vacuum. The vacuum was generated by the intake of the engine. Easy to trace and fix, usually a broken vacuum hose. Worse case would be the cylinder diaphragm is busted. Either way it should be easy to fix.
Later years they switched to electric. My 1979 is electric. It has a dc electric motor that moves the rear between high and low just like the vacuum cylinder above. The motor is controlled by two wires, red and black. The two speed selector switch receives power via a green wire. It applies power to the black wire for low speed, and the red wire for hi speed. The black wire also feeds power to an electric speedometer adapter unit, in line with the speedometer cable, to adjust the speedometer gearing when in low. The motor and speedometer adapter both must be grounded. Do not apply power to both the black and red wires at the same time or you will let the smoke out of the motor and it will cease to operate.
On the electric unit, the first place to start would be the fuse panel, looking for a blown fuse.
Here is a link to my two speed rear end. I upgraded the gear ratio by changing the ring and pinion.
http://67-72chevytrucks.com/vboard/s...d.php?t=729084