The Stovebolt Site Forums The Parking Lot '60-'66 Trucks 1960 heater controls

Not exactly sure what you want to do. Just get hot air or take it apart and rebuild. If you just want hot air, you probably have a heater valve operated by a cable. Then you have vent butterflies operated by cables. So three cable levers and one fan speed lever = 4. Disconnect the two cables from the heater plenum butterfly levers inside cab. One for air/recirc and another to direct it to cab or defrost. Move these flappers to desired position. Third cable goes to a water valve lever. (heater valve). Core and valve could be inside or outside cab depending on heater ordered. Disconnect and operate to let water in. If none of that is possible, start removing screws till it comes apart, inside and out. Depending on which unit you have, it's pretty obvious how it need to come off by examining it.
I have a 1960 GMC with similar unit. Some are standard and some are deluxe. If your core does not leak consider yourself lucky, until it does. Post some pics if you want more help. If you have a valve and it's no good, you may be able to bypass it and put in an aftermarket cheap valve in series with one of the hoses.
Sounds like you have deluxe heater that will have core, motor and valve on outside of firewall. The inside is just plenum/air routing. Outside stuff is where all the action is.