I have the same problem, no heat in the 60. I tried flushing it out but without much luck so i bit the bullet and tore it out of the truck,,,three words DONT DO IT. It was the biggest pain in the ass that I ever went through, after 3 careful hours of unbolting piece after piece I finally got it out. Its a long long story but at least now that I have everything apart i can clean out all the ductwork, replace the broken fresh air cable etc etc.
Now i see why my mechanic wanted 16 hours to do the job, I still do not have it put back together and by the time I get around to it I will have forgotten how it came apart.
TRY THIS instead..
-replace the heater valve in the engine compartment, aftermarket JT outfitters 30$?
-replace the thermostat and make sure that you install BOTH upper and lower gaskets, the upper being a round gasket.
-FLUSH the bugger out- remove the upper and lower heater hoses that connect to the core at the firewall. Buy and install a section of heater hose with a flush out adaptor that allows you to connect a garden hose, connect it to one of the heater core thin brass tubes @ the firewall-flush it out.
The only problem with flushing the whole cooling system is that the heater core has the smallest passages and therefore will clog up with all the crap your flush has loosened. Depending on what is causing the problem, you could remove the heater core and join the hoses going to it with a piece of copper tubing, then flush the system with a caustic and drain/flush again, drain. Clean the heatercore with an acid, I like CLR(calcium, lime and rust remover), then reinstall everything.
Before you do all this, get the engine up to temp and turn on the heater, feel the hoses going to it and they, at least one, should be hot. If not, the thermostat or the heater valve, as mentioned, may be the culprit.