I need help rewiring a pre-1950s Mimms lowboy fan. Any advice on rating the cap (3speed coil) and 4-pos 3-way rotary switch
That looks like a tapped inductor, presumably in series with the motor. There is probably nothing wrong with it. Just replace the insulation on the leads.
A substitute might be possibly made from two separate inductors but it is highly unlikely that a similar replacement exists.
If the wiring is too degraded you could carefully take it apart, while counting the turns and rewind on the same core. Make sure you remember how the laminations were assembled. Inductors and transformers are arranged differently.
What you say is leaking is probably just the shellac that was used to insulate it when manufactured. Most inductors and transformers of this type are submersed in an insulating compound, similar to shellac, and then baked to cure the shellac, ensure all water is removed, and prevent buzzing or vibration. It is common for such transformers and inductors to last a hundred years or more.