This is a gas heat. A Payne furnace, vertical unit, with the E.coil on top.... feeding into the plenum.
That time delay relay sounds interesting. The tech did notice it... and said it was say way high. However - when it is not cooling well - the compressor is running. It is doing it right now - I went outside, and without question the compressor is running... but it doesnt seem to be compressing. The liquid line isnt warm and the coil isnt putting any heat off right now. The previous cycle right before this one was great.
The system does this randomly. There is no pattern I can find. Sometimes it will do it on the first cycle after turning it on after being off all day... sometimes it will be the second cycle, sometimes it wont do it at all. When the tech was here we cycled it many times and it never failed.