I pulled the selector switch and valve from a mid eighties truck and used it on my '75, so I probably have the same setup as your '82.
Do you have a rocker switch in the dash that just clicks in either direction and holds (which I have), or does it have the word "depress" so that it pushes down and then returns? My switch just clicks in either direction (simple rocker switch).
Assuming that the left side tank is your primary (on my older truck the right side was primary)
There are 6 terminals on the back of the switch and it is split into two sections. One half has the middle terminal connected to power and the other half has the middle terminal connected to the gauge.
Switch to left side tank -
-- middle gauge terminal connects to wire running to left tank
-- middle power terminal is open (no power to solenoid), which means you are now on the primary tank
Switch to right side tank -
--middle gauge terminal connected to wire running to right tank
-- middle power terminal connected to solenoid - powers the solenoid and switches to other tank
If the tank fuel feed does not switch, its a solenoid problem. You need to check for 12 volts on/off at the terminal that pushed onto the solenoid. You also need to plug it back in and listen to verify that the solenoid is operating.
If the gauge reading does not switch, its a problem with the wire running from the switch to that tank.
There is more wiring than you would expect to the sending units because it is a universal loom that allows for either dual or single tanks on the assembly line.
Bruce