I tried my wing de-ice lights the other day on our 1961 C-310F and they don’t work, so I ordered new bulbs from Aircraft Spruce and they still don’t work. The airplane has the alcohol props (currently inop and will stay that way), and is plumbed for boots, but currently has no boots, and won’t as long as I own it.
As I looked at the CB panel, I don’t see any label that says that the de-ice lights are wired through any specific CB on the panel.
When I looked in the illustrated parts list and Service Manual, there was very little info about this circuitry.
I would suggest using a Voltmeter to check and see where power is getting to. I would check the bulb sockets, and then the switch. When is the last time they were working? If both lights are out, but worked recently, it is much more likely to be a hidden fuse, or issue with the switch itself. I am not familiar with the 310G, so I am not sure where you would look.