My shower light is very much right above the handheld shower:


A headlamp would work to some extent for getting stuff out of storage compartments, but isn't as convenient as lights in the compartments themselves IMHO. Some reasonable restraint could be used; if the only thing in a compartment is the shore power cord, you probably don't need a light there to find the cord. Likewise, there's little need to study the propane tank in the middle of the night generally. It's more handy for spaces that need more extensive scrutiny, such as general storage compartments.
I would not suggest a 120V light as the main outside light when there are plenty of 12V lights that work fine, since using the light would require either being connected to shore power, running the generator, or operating an inverter. I would definitely not suggest wiring up a 120V outlet with 12V power as you or someone else will get mighty confused at some point.