Two problems. First is varnish, second volatility.
"Varnish" is taken care of by the stabilizer, or in most all modern fuels, by the detergent additives in the gasoline designed to keep your injectors clean. Little flapper valves can stick and Venturi diameters change with accumulation of "varnish."
Other is volatility, where - alcohol "dryers" don't read this - the more volatile components in your gasoline blend evaporate more rapidly, and change the blend toward the heavier components. Makes it tough to get a start with old fuel sometimes. The ether trick is the most common, and you can usually save the old gas by mixing it with new to get it to useable vaporization rates. Injectors don't seem to mind it so much as carburetors, so your car is a good place.
In short, drain and purge the carb for storage, or use an anti-varnish ingredient. If you do the latter, evaporation will eventually drain the carb for you, with potential for leaving behind "varnish." Empty carb is why long-stored saws take three-four pulls or a prime, if so equipped.
I just purged and oiled the piston in my snow blower Wednesday prior to moving him to the shed to occupy the space made by removing the mower.