1.) It depends on which Peavey you have.
The old 1970s/80s sometimes had very special pots for tone+coil split ...
2.) But your description sounds like a normal tone pot ...
The pot has nothing to do with tone or volume. These are (often) the same and are only for the regulation. The capacitor is the important thing to turn a pot into a tone pot ...
So, I would say the capacitor is broken. If it had a short cup, the pot would work like a volume. If it is broken (no connection inside), it doesn't work at all.
You should get a new capacitor (22nF to 68nF is normal) for some Cents ...
A standard capacitor has 47nF / 50nF which is also called .05µF ...