Is there a "special" oil for Sturmey-Archer 3 speed hubs? Was going to add sewing machine oil in the port.
Yes indeed there is. No SA hub will work without it. Yours for $200 for an NOS can. (ballpark estimate from pbbikes)
But seriously, just don't use vegetable based 3-in-1. You can use the dino version, I think the can is blue.