This seems like a silly question, but here goes. I'm on contract for 13 weeks. I've got mail forwarded here and will be putting this address down as my "permanent" address for certain things until I otherwise have somewhere else to go - but what about my driver's license? And voting?
Well what about it? An address of convenience is as simple as renting a mailbox. If that is all you need, one way to learn the nuances is reading "fulltimers" subforums on RV forums - those guys need mailing addresses and voting rights but their only home is mobile.
You may be missing much larger issues. Without a permanent home you are working away from, you are an itinerant worker (wherever you are is home), and are not eligible for tax free housing, travel, and per diems (meals and incidentals). The tax savings can in many instances more than pay for upkeep of a permanent residence.
If you are working under a compact license, that may not be valid unless you reside in that compact state.