I just put a new heater core in mine (a 64) when I bought it because of the mouse smell. The new one weighed half as much as my old one due to the clogging. Even this morning at -15 degrees, I had to turn the heat down about halfway to work. Don't try flushing to old core, it will put out marginal heat at best compared to a new one. Besides, your 61 is probably the easiest truck there is to put a new core in,
Scott