I've got a Magic Chef furance/blower from the early '80s. When the thermostat calls for heat, an ignitor starts clicking and a steady pilot light comes on. The clicking will continue for about 10-15 seconds, then stop. After another 5 seconds, a different click is heard (gas shutting off?) and nothing happens but the pilot light stays lit. I did see one time, during the initial clicking, the two burners fire up fully only to poof off after about 5 seconds. The furnace had been working fine when we used it once or twice a week over the last month.
After some research, it appears the pilot light is lighting just fine, but perhaps the flame sensor is dirty or bad? I'm not able to tell where the the flame sensor is in this model to check though. Any other ideas on why the burners won't light? I know this is one is old and probably either needs cleaning and/or replaced. Here are a couple close-up pictures if it can help to identify the flame sensor or other problems.