I believe your second option is best. Keep the fuel level as low as possible and add a small amount of fresh gas and some fuel stabilizer when needed.
I have seen what can happen to an engine that burns old gas. I once had a truck that was used occasionally to haul things, but it mostly set around waiting for a need. Folks would borrow it and often generously fill the tank as payment. Eventually the engine became so varnished up, the intake valves stuck in their guides and bent the push rods, and before that happened the rings would stick for a few minutes, blowing blue smoke until the pistons warmed up enough so they would seal. I had to overhaul the engine.
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