Hallo Per,

high current contacts in a switch or relay are made of a certain material guaranteeing many switch-on and -off conditions, before failuring. But they are not suited to reliably switch very small loads, also called 'dry loads'.
You have two options: Using gold contacts guarantees reliable low ohmic contact resistances even with dry loads, but they burn away with the first heavy load. The other option is to have cadmium-oxid or silver/nickel contacts, guaranteeing reliable switching of heavy loads, but completely unable to handle dry loads.
I don't know your certain switch, but I highly assume, that there are no gold contacts, but certain heavy load contacts. So, you will not succeed with dry load switching.
For JH-relay from SDS, e.g., which is a 30A 380V relay, mimimum switching voltage is 10V and minimum switching power is 1W(VA). So, you would need at least to switch a 100 Ohm load connected to 10V, for fullfilling specification.

So, don't forget, that not only miminum voltage is needed for reliable switching, but also minimum current!

By the way, this has nothing to do with old and dirty contacts. It's just the physics of NEW contacts!

Bye,
Kai