It's one of the four DC motors that the F4 uses, the one that charges the aperture lever AND one cycle of set of shutter blades.
I've had this happen twice to one body, fixed once, and once to another body. Still awaiting diversion of repair budget on that one.
Funny enough, my former shooting partner with two F4 with nearly same amount of wear (5-7 years of hard wedding use) it has not happened.
I attribute this to my use of Continuous High motor setting *every time* and her use of Single *every time*.
As I know it and you can search it, the stepping of the motors is different in S, Cs, CL and Ch.
I'm certain that my constant use of Ch has led to this.
I didn't know that the motor does the stop down of the lens. I thought although the motor would charge the shutter mechanism but then after that it's spring operated. I love the high speed motor drive in both my F3 and F5 but I never use the continuous mode. I always have them on S mode.
My F4 had the same issue; it took me a long time to figure it out. I eventually jammed the depth-of-field preview button in, and shot it that way for years. Good times. If you don't want to MacGyver your camera like I did, you can still meter and shoot by remembering to press the depth-of-field preview button during exposure.
This happened to my F4 that I've had from new. I unknowingly used a lens on it that had oily, sticky, stuck aperture blades. Repair cost on the body's aperture control mechanism was less than $200 if I remember correctly.
Not sure if you had fixed this. I had the same problem and solved it like this:
1. Remove the lens.
2. Take some lighter fluid and a small paint brush.
3. Dampen the brush with lighter fluid
4. Brush the inside of the lower shaft.
5. Do this again on the shaft on the left of the mount.
6. Put the lens on.
7. Stop down the lens manually a few times.
8. Set the aperture on the lens at minimum.
9. With the shutter set to 1-2 sec, fire it and watch the aperture blades.