Rod spins with the clutch basket. Say when you hear the squeak, you ever so lightly pull the clutch in. But what you are doing is loading the rod so it stops spinning. If it goes away without taking the slack out of the cable, my guess is back to a dry ramp hole, or where the rod is centered in the ramp assembly.
So say I meguyveer over to the auto/hobby store, find a plastic tube that can slide down the same channel as the pushrod, have a wooden dowel that can fit inside the plastic tube; fill the end of the tube with grease; shove the greased end down the channel; slide the dowel down the dry end of the tube and push the grease into the clutch cable ramp assembly where the rod end is located.
Rather than pull the cable assembly, find a gasket, change the gear oil, etc., this is the loophole greasing what I think might be a dry rod spinning in the housing.