Well, my car (a '71 GT) has a non-lighted switch that is either on or off, no middle position, just like the hazard or heated rear window switches. (Of course, maybe the later switches like yours only go to the middle, I dunno). Anyhow, I think you overestimate the heater in these cars. I have repeatedly seen them refferred to as "a wisp of a heater".
That being said, I just rehabbed my heater significantly by fixing the rotary switch that controls where heat is directed. When I got the car, it seemed to do essentially nothing, so I removed it (easier said than done) while I had the A/C out for dash bulb replacement (new halogens from lbcarco.com go in tonight!). Basically, I had to fiddle with the stops to get the gears in position so that they stayed enmeshed in both the on and off position. Then, when refitting the cable, I made sure I found the full extension and full retraction and did my best to make sure that those points coincided with the "Off" and "Screen" indicators on the switch.
Long story short, I now have actual air emitted from my defroster vents when I turn it to screen, and no air infiltrates through the heater vents on the floor when I have the switch set to "Off" (which is a nice feature on hot days with a hot engine!). I am a very happy camper, and you might want to look up under your dash and see if the cable is moving as it should.