Fuel stabilizer does very little and is unnecessary for just one winter. What you should be far more concerned with is ethanol, and ideally you should be putting in ethanol-free gas for winter storage. Watch this video to find out how ethanol will rust out your fuel system from the inside out. Fuel stabilizer will not stop the corrosion damage from the ethanol in your gasoline.
https://youtu.be/UvS_D4_lF5U
I know ethanol-free gas is a little hard to come by in California, but Jay Leno talks about where you can get it:
https://youtu.be/DL_8SkZjEPc