Perfect pulsing lights

So a few days ago I turned on my daughters ceiling fan light and the light started to blink in a perfect pulse, about two blinks per second. The fan seems to work ok. So I went and bought a new ceiling fan today to put up because I figure the light power is bad. Then, this evening I went up to change it and turned on the ceiling fan in the loft and the same thing happened. Perfect pulse blinking. Both fans are about 15 years old, but different brands. Now if I remove the LED bulbs in the loft and put in normal ones it works fine. This fan has a twin on a different breaker and has the same LED lights and works fine. I suppose it could be a super coincidence, but unlikely. I changed the bulbs in the initial fan and no difference. The fans are on different breakers and none of the equipment on the on those breakers is working incorrectly other than the lights on the fans. I’ll change the light switches on the wall tomorrow to see if they are coincidently both bad. Any input would be appreciated.