Socket looks like a standard "2 Form C" layout for 10 Amp relays.
Can you determine what the coil voltage is?
I have 24VDC and 48VDC coils for relays of this size. But you're probably looking at a 120VAC coil.
If it's a 120VAC coil then that would be something like a P&B part number K10P-11A15-120.
And... the more I look at it, it can't be an AC relay -> it has a back-EMF diode on the coil.
Need the relay coil voltage either from manual or measured voltage to get part number.