I lived in Ca. You can put a camper or shell on a pickup and register it as a non commercial vehicle, but if you then take the camper or shell off, it is ticket time. If you stay in the same place in Ca. and have out of State plates, they can cite you with a fix it ticket and make you register it in Ca. after a month or two. You could fight the ticket in court, but Ca. is no stranger to people avoiding their taxes. Judge may say show me evidence it is normally kept out of State. How is it you spend the majority of your time in this State but your registered in another?
Sure Arizona will let you register with a friend or fake address, but that won't protect you in California.
BTW Ca. also has a law that says all flat bed trucks must stop at weigh stations. It doesn't say unless empty. They might want to do a safety check on you, (brakes, tires, horn etc.), If they find something wrong, you are not going anywhere without it being towed to a shop.
http://www.dot.ca.gov/trafficops/trucks/weigh-stations.html If the pickup has a GVWR of 11,500 pounds or more, an unladen weight 8,001 pounds, not equipped with an open-box type bed not exceeding 9 feet in length, or the pickup bed has been removed and a utility body or flat bed has been mounted, then it no longer meets the definition of pickup in CVC Section 471; it is then a "motor truck" under CVC Section 410 and required to stop at the weigh stations.
Soooo glad I moved to Nevada.