Right side EGT normal then drops at idle

EGT probes are known to be limited in life. Erratic readings is one of the first symptoms that they need replacing. If one is bad, replace both because the "good" one will soon start giving problems. I noticed that when I replaced both of them at the same time, my readings suddenly became much more matched between the two. Even before they go noticeably erratic, I believe they start losing accuracy.

A loose wiring connection can cause it to drop suddenly (within a second) and intermittently.  An open circuit on a thermocouple circuit will give a reading close to ambient.  A high resistance joint will give a reading that is noticeably lower than the other EGT but still well above ambient.

Check and/or remake the connections on that circuit.  Don't touch the other one if it is working, because you don't want to introduce a fault into that one.   ;-)

Low EGT on one side during flight might indicate carburettor icing, but you would probably hear or feel rough running.