Random injector pulse cylinder 5

A while back my old 2002 sable (vulcan engine) started carrying on as I was driving and it started flashing computer light, which is a sign of something not good. I pulled over and it started making a loudish noise like a large air compressor(best I can describe). I shut it off, looked it over and restarted. the noise was gone but had bad mis. Got it back home and had misfire codes on cyl 2-5-6, but noting else. I checked the plugs and cylinder 5 had the platinum tip missing...I can only assume it burnt up or fell off. Replaced plugs, and still had cylinder 5 showing misfire. Seemed to be almost constant. I checked injector for ohms and volts....checked fine. However when I used my stethoscope (Advance el cheapo) I found that the injector is working randomly. I was hoping it was a case of damaged or clogged injector
but I ran a test with a noid light and find that the injector is getting a random pulse. basically it works for 20-30 seconds then shuts off for 10-30 seconds. On open road and acceleration it seems fine but at idle it still sets a cyl 5 misfire code and so now I have to look elsewhere. Although it seems to do this after it warms up I see that the engine cooling fan kicking on and off can also occur about this same time so i suspect a loose ground or bad computer.But I am not familiar with exactly where and how this all works on this car and probably the first cat I have had in a long time I dont have a service manual for....Anyone have an idea where to start looking?