I have an old York furnace with central air. When turning on the A/C, sometimes the blower comes on, sometimes it doesn't, and sometimes it toggles off and on with a loud clicking sound. If I use the manual switch on the limit control, everything is fine, but of course, then the blower is on continuously. Taking a look at the system, the problem seems to be what looks like a transformer with relay and lots of various colored wires. From reading previous posts and checking the internet, this stuff seems to go by names like A/C relay, fan control, fan relay and the like. I know I could just start pulling out wires and taking the whole thing off, but is there a specific part that is going bad? Is that loud clicking sound a failing relay?

Usually the continuous fan uses the same relay as the A/C. I would look at some of the connections, with the usually color codes, the yellow and blue wires and what they connect to within the furnace. There should be a timer that keeps the fan running for 90 seconds after the compressor quits.

A voltage detector is great for stuff like this. The tip on them lights up when you touch a live wire. Touch the in and out wires to a relay or other trouble maker, and if the in lights up, but not the out, you have found the problem. I paid less than $15 for a GB instruments Live Wire, GVD-505A.