Is it possible to wire a 120v light off of a 220v compressor?
Don't worry about how to wire up a 120v bulb - just get one that is designed for 220v.  Half the world uses 220v for lighting and general purpose outlets, so it's not hard to find online.  If you want to find something in a local store, look closely at the boxes for LED bulbs.  They could have a power supply that supports a wide range for the global market.

If you want a certain type of bulb, look online.  You can find LED or incandescent with a variety of bases.

And to add in other answers from the comments - a timer might be a good choice for you.  Home stores commonly sell large mechanical timers for 220v water heaters.  They should work well on something like an air compressor (assuming it is less than 40A, larger timers might be more rare).

And of course the other option would be to fix all the air leaks so the compressor never runs.