We'll start off with these two questions first. Say I buy a house north of Vegas. I find a LGS in Vegas or Henderson, and attempt to buy a pistol. However, my legal residence is still HI. Isn't the background check still in NV? Am I constrained to a 10 round mag or a higher limit which NV allows? The ATF form which we fill out seems to ask for the state where we legally reside. This is government trick which may be used to get a search warrant for the HI residence, at a future time.
Legal residence is a status with ramifications that are tax related and gun related. HI allows tax breaks to residents that are not available to non-residents. Also, this has nothing to do with the number of days you're present in each state, so I don't know why you bring up the 50-50 question. Your 1040 return and voting card have a higher precedence than days in state.
You really should study the federal and state (HI) laws more. You tend to ask lots of questions, and most of the answers are there -- at least the issues are addressed if not really solved.
Federal law will not let you purchase a handgun in another state (intrastate purchase) without shipping the gun to an FFL IN YoUR HOME STATE.
Once the gun arrives in Hawaii, the Hawaii FFL (not the NV one) will be responsible to make sure you comply with HI laws. That means you need to present a valid Permit to Acquire. That means you have to undergo the HI background check and 14 day wait.
Long gun rules vary, but in most cases where an FFL is the seller, they must be satisfied you are not breaking the laws of your home state. So, if you live where AR-15s are banned, he can't sell you one. If you're required to present a valid long gun permit to acquire in HI, you have to present it to the NV dealer. All depends on the state's laws. In general, federal law is the governing rule, and state laws can either follow that or make more strict laws for themselves.
You really went off the deep end with the legal residence rabbit hole, huh?
The only purpose of declaring your legal state of residence for gun purchases is for interstate commerce and NFA compliance. If you have a valid FFL dealer license, you can transfer weapons between states. If you have Collector's C&R FFL-03, you can transfer qualified weapons across state lines without having to go through someone with a dealer FFL.
The whole intent is so DocMeercy can't live as a New York State resident, then hop in his truck, drive to Virginia, and buy a gun out-of-state in order to bypass New York's gun laws.
Unless the seller from out-of-state is willing to risk his FFL license (if he is a dealer) and/or prison time for selling a gun to someone who's not a resident of their state without shipping it to an FFL in your state, the system pretty much works. What it doesn't do is stop criminals from buying guns in one state and selling them illegally in another state for a huge profit. Both the buyer and the seller are risking some hefty penalties if they get caught. And, if you aren't already a felon, doing these crimes will make you one, meaning you won't be able to buy or possess a firearm legally from that point on.
"Legal residence" is defined based on whichever body of law you are referring to. The IRS definition is NOT the one the ATF uses. If you're military, and your legal residence is NC, but you're stationed in OK, guess which state's laws you must comply with when buying a firearm?
Hint: It's not the one to which you owe state taxes.