AC Induction motors use an internal squirrel cage with skewed bars for the stator... However no matter how hard I look around on the internet I cannot find an external-cage AC induction motor design, except for a mention about ceiling fans using them. How would the wiring differentiate--if any--if you utilize an external cage vs an internal cage? How would torque output change with a larger cage as an outer rotor?
Small AC fans often fall into that category.
It's cast as a bell shaped rotor, but you can see the skewed bars of the "cage", apparently formed by aluminium flowing into slits in the laminations during the casting process. These laminations contain the magnetic field quite well, but I can't put a figure on how close it is to the traditional internal rotor.
The "shaded pole" structure is not so clearly visible in the wound stator, hidden in the green resin (but you can see a longer pole, and a slit by the shorter one)
Such motors typically don't have a squirrel cage but a massive bell-shaped rotor. Wiring is no different from an internal rotor induction motor.
Starting torque is low, and the torque over speed curve has the typical huge hump because of the massive rotor. Really only suitable for fans and pumps.
They come with a running cap usually. I have yet to find a shaded pole variant. Most likely the starting torque would be much too low then.