Is a dedicated circuit to gas furnace always required?
Put a subpanel here

Provided there's enough clear working space out from that side of the furnace, you can replace that fusible mini-disconnect (switched fuse cover) with a small subpanel (a "spa panel" type of disconnect is large enough for this job, although GE makes? or at least made the TL510RT that is basically perfect for a 120V only application if you can get it, and SqD has the QO24L50TTS that will do the trick here as well), that has 2 15A breakers on the same leg, one for the furnace and one for the other circuit.  (You can also put the service receptacle for the space on this panel, if one is not already present.)

Or, if this is all in conduit...

If this circuit is run entirely in conduit, then there should be enough space for another 15A circuit (hot+neutral) in there for the remaining loads, allowing the furnace to be left alone on the existing circuit, or vice-versa, with the furnace moved to the new circuit and the other loads left on the existing circuit.