As I recall, that pin should be retracted and the head turned 90º to lock it in the retracted position. But it's been several years since I had a IIC. At full height, the lens cluster is going to be fully retracted. If there is crud in the focusing rails or perhaps due only to a "sticky" bellows that doesn't want to extend, the lens cluster remains "stuck" at the top of its travel instead of tracking the cam as intended. Then when the forces equalize, gravity does its thing and the cluster drops to find the cam once again.
That, at least, is a possible scenario. I recall something similar happening when I had mine. But that was >15 years ago and memory starts to get a bit wonky. "Curled" really threw me off and it wasn't until I looked closely at the pictures that my old neurons started firing again. Curled ≠ knurled!
Again, check the travel of the lens carriage and make sure that it is smooth throughout its range and that there is no foreign objects or debris for it to get hung up on. Something as simple as some dried grease can foul the works. Those Germans worked to pretty close tolerances.
That Focomat IIC is one of the most over-engineered things I've ever seen. Right after the Linhof Technika.
Their insistence on having a sliding lens turret really put some design restrictions on them. Consequently for us, the IIC cannot utilize standard modern enlarging lenses. And ironically the Leitz lenses are a weak spot of the system. (Yes, Leitz! Hard to believe!) I had the 100mm Focotar-2 lens and could not ever get the corners of my negative in focus at the same time as the center. I used several different test negatives of my own making, along with regular unmodified images, but was confounded trying to get everything in focus. Fortunately I was still able to get reasonably good prints. But it was a disappointment.
The predecessor to the IIC was the IIA. Focomat IIA enlargers prior to 1950 had a single mounting point with a helical focuser and to change lenses, you had to unscrew one lens and screw in the other. But that way you could choose your own lens. Back then not so much, but today with the range of excellent enlarging lenses on the used market, that's a neat system. Unfortunately back focus distances and aperture rings of varying sizes makes it challenging to make it work. But IMO it was a better system than being locked into a proprietary lens by the manufacturer.