Victor Hugo didn't care exceedingly about writing credible stories and readers don't complain. But I appreciate that your care about.
Flame from a battery and a gum wrapper looks OK. Not every wrapper is said to work. The metal layer must be extra-thin on the paper. Batteries make also sparks, which may suffice with a few liquids like gasoline.
Wood gets damp in a cave. The former users must have protected it.
Whether moonshine catches fire from a small paper? This depends on the concentration and the wick (the character's shirt). For instance rhum, with 40% alcohol, must be hot to catch fire without a wick and make crêpes flambées. I expect a shirt soaked in moonshine not to light: it takes an intense source to heat and evaporate some booze first. Better ignite first a dry part of the shirt, let it burn until the flame reaches the soaking booze. I suggest to experiment that with 40% vodka. If it fail, synthesize some 70% booze by mixing pure ethanol with varied amounts of water.
Pharmacy cotton is very easy to light, but it burns swiftly. You need paper to follow, then very thin wood, followed by less thin, and so on, all dry. Pressing the cotton together lets it burn more slowly but it's difficult to control. Cork burns but not so easily, it can be a step before wood, not an early step. Cotton is also a nice wick. My suggestion: the users of the still had all the material kept dry on site, only the lighters not.
Had the users of the still some wax to seal the jugs? That makes better light that a soaked shirt that is difficult to hold and burns at uncontrolled speed. With a wick, it's also decently easy to light, more so than wood.
How does your superhero organize all that in the dark? Is the chamber with the still less dark?