J1 is a coax push-in connector from an Icom FR4000 repeater. The gray wire is a thin piece of coax, unsure of the actual type (RG316?). Not a common connector but I've seen it before. Doesn't click in, just pressure fits in there.
I'm trying to make another pigtail so I don't have to cut the gray coax to add an N male connector on the other end. The manual recommends modifying the cable but I'd rather just make another one and keep the original intact to revert back.