the Washington and Oregon Tax Nazi's have long ago gotten smart about the 'living on the border ' truck. They actually have the equivalent of 'border' guards to catch stuff like that. Like cars purch in one state but living in another etc. It could be an urban myth but knowing how the tax collectors don't want to miss a trick it makes sense.
We used to go south to shop and avoided taxes by showing our driver's license. They wouldn't tax us as we lived in Alaska. They do now. Which is correct anyway. It is where the transaction takes place, not where you live.