Nikon FE meter turns off when on f4, but all other apertures work fine.

I have a FE that when I use F4 the meter seems to shut off. At any other apeture, everything works fine. I am the original owner of this camera and it has never had a problem. I am wondering if any one know what the problem is.
The aperture ring moves smoothly, the batteries new and correct, but this is the only anomaly.

Does anyone know to what the aperture ring attaches so that the meter works. I am guessing it must be something wrong with this part. Something like a variable resistor, potentiometer, or ? How difficult would it be to fix oneself, or how much is likely to cost to repair?

Any insight is appreciated.

Rotate the aperture ring back and forth several times, move the ASA ring back and forth a few times as well as the EV adjustment. Often the contacts just need movement to "wipe" them.

Try that first.