I haven't seen somebody mention this but in Arizona and NM in the northeast and northwest corners specifically, its the Najavo reservation. This is Federal land, and you cannot conceal carry through this. Guns have to be unloaded in the truck and ammunition in a separate container.
Do not keep any guns near the front of your vehicle within reach.
All I will say about this is, if you are traveling on a Federal, State or county roads it is legal if following laws for the state you are in; that property is a right-of-way owned by the respective government. Basically, true for all Indian lands throughout the USA. However, once you pull of the Fed, state, or county road onto a road owned and controlled by the respective tribe....you could lose your weapon if stopped. That's about all tribal police can do to a non-res resident. They could hold for federal authorities but MOST LIKELY won't. Just take you gun and escort you off the lands. And only way you can get it back is to sue, but the tribe, being their own gov't entity can refuse to be sued. Similar to many gov't agencies.
I currently carry through an Indian res quite often; however, I stay on the state highway.
When I lived in UT, I had a few Tribal police friends out of Monument valley. Navajo Tribal Code Title 17, Section 1451, prohibits the
use of firearms. The Navajo nation understands that many of the people who travel to the reservation are traveling legally with handguns. When entering the res on one of their roads (possibly to take the 17 mile scenic road through the park) so unload, lock up and there will be no problem. (I am not speaking for the Navajo res, just understand their policies, requirements and wishes, and it is their land.)
And really in some states it is next to impossible not to go through a res. I-40 through OK is notorious for going in and out of reservations. Highway 163 goes right through Monument Valley; just don't pull off at Redlands Grill, regardless of how great the Fry Bread is! (And yes, it was the best!)
However, this is far from legal information and in fact, I have not been in SE UT or any res in UT, NM, AZ since approx. 2016, things do change in res laws/policies as they do at state/federal levels.
So if in doubt, just unload and lock up, call the res, contact the state AG or state Police, etc.However, it is most likely not required.
I know for my travels, I just continue to carry concealed through any of the reservations near where I live.