Personally, I would keep my gun loaded and on my person in New Mexico. Which is perfectly legal in New Mexico without any permit at all - so long as it is not concealed.
If you do want the protection of Federal law, should you choose to take advantage of the Firearms Owners Protection Act, simply lock the unloaded gun in the trunk with the ammo in the trunk as well. You can even leave your magazines loaded. If you follow Duke's advice and separate the ammo from the gun by carrying the ammo in the passenger compartment, the Federal law (FOPA) will no longer protect you because you have now violated the provisions in FOPA.
18 USC 926A:
Notwithstanding any other provision of any law or any rule or regulation of a State or any political subdivision thereof, any person who is not otherwise prohibited by this chapter from transporting, shipping, or receiving a firearm shall be entitled to transport a firearm for any lawful purpose from any place where he may lawfully possess and carry such firearm to any other place where he may lawfully possess and carry such firearm if, during such transportation the firearm is unloaded, and neither the firearm nor any ammunition being transported is readily accessible or is directly accessible from the passenger compartment of such transporting vehicle: Provided, That in the case of a vehicle without a compartment separate from the driver’s compartment the firearm or ammunition shall be contained in a locked container other than the glove compartment or console.
Personally, I would just keep the loaded gun on my belt, where it belongs.
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