From what I was told whenI visited AZ some tribes will honor your permit and others won't.
You can contact the AZ DPS or the Tribal police to find out if your okay.
Or secure the firearmper Federal peaceable journey law and hope you are okay.
SinceI wasn't planning on stopping on the reservationI just did whatI normally do.
I have heard from others that the reservation should be treated like a foreign country and assume your firearm is unwelcomed.