One Monarch 10EE owner describes the pot as:
"58C1 Clarostat with half of the windings shorted."
By "windings" I think they mean it's a wire-wound pot.
Since the pot is dead, I would disassemble it and see if the resistive elements can be repaired or replaced.
There are also two still available from this set of 5:
https://www.ebay.com/itm/324730119011