We're passing through on our way to the Grand Canyon from Atlanta.  I tried to scan all the states on handgunlaw.us for the key factoids (which I summarized below), but please help me with anything important I may have overlooked (or anything I have wrong below).  Sorry for not reading tacked threads on local laws, but I'm having to do this for about 10 states on this trip.

1) Reciprocity with GWL - NO
2) Must Inform - NO
3) Sign = Force of Law - NO
4) Capacity limits - NO
5) Park carry - NO (no reciprocity)
6) Restaurant w/alcohol carry - YES
7) Store w/alcohol carry (ex: Walmart) - YES

How should I plan to handle my pistol while exiting the vehicle to pump gas, get food or when camping (Santa Fe KOA)?  Thanks in advance!

Since NM doesn't recognize your GA permit, #6 and #7 are BIG NO NOs. No carrying in any restaurant that serves any kind of alcohol and no carrying in any store that sells any alcohol (walmart, most gas stations, etc)

When you get out to pump gas or go inside someplace, you'll have to leave it locked in your car.

IF you have a permit with reciprocity, you can carry into a restaurant that serves beer and wine ONLY. Hard liquor is no go (derp). You can't drink at all while carrying anyways. You can only concealed carry 1 firearm at a time. Signs carry force of law, however you must be asked to leave and can only be arrested or cited if you refuse. Open carry is g2g here. Just consider that the cities are full of easily frightened sheeple.

Good point.  I guess I meant those were YES "if possessing a valid carry permit", which I won't.  We're planning a nights stay at the Santa Fe KOA, but I don't think we have any sight seeing planned yet for NM.

Can non-residents open carry?  That would solve my problem of securing my pistol when outside the truck getting gas or lunch, or when camping.

Yes

And now is the time I feel the need to point out something to be careful of.  When on a reservation, the laws are different.  This would include places you might sightsee or get fuel.  What those laws might be differ from reservation to reservation.  I think the generally accepted consensus is "don't let them know you have a firearm and don't be an asshole".  Pretty sure this has worked for most.

But be aware that most gas stations in NM sell beer, so you have to be careful if you go inside to buy a snack or drink or use the restroom while open carrying

Fair enough.  I'm going to print all this info per-state and stick it in the dash, because I won't remember it all.

Smartest thing to do on any res is to just leave it in the car when you get out to pump gas, buy jewelry, etc.  Talked to a cop on Sandia reservation and he said they know you have a CHL if they pull you over or just  run your license, but they are directed to not do anything if you leave it in car while outside of it.  He also said you not being able to carry it is the stupidest fucking thing on the books.

while you're off camping in the middle of nowhere OC should be fine, never had a problem.  But I wouldn't recommend trying it in the cities, especially Santa Fe....