If you run a 12V landscape line you won't need to trench that deep, and you can put an AC timer on the 12V power supply back at the building itself. This means your sign will light up even during a week of cloudy weather.
Another option is just to use all-in-one solar landscape fixtures that can be adapted for signage. No battery, charger, inverter, or timer required.
Personally, I'd prefer a AC GFI because a convenience outlet near the entrance might be useful for certain kinds of events. If there's a utility pole nearby you might be able to get a separate meter drop to your sign. You'll need to do your own conduit work back to the pole, but the utility treats it as a second account to the same property - not much different than a duplex or attached condos.
Of course, lighting up your sign usually has to also have code approval. Being approved for a sign versus a lighted sign are two different cases.