I'm from New Mexico. There is no CCW, for anyone, period. It's one of the 7 or so "no-issue" states. However, open carry is legal, with the usual restrictions on bars, banks, courthouses, etc. In my 21 years there, I think I can remember seeing 2 people with openly carried guns.
In NM, your car is considered an extension of your home for the purpose of storage and transport. The gun can be anywhere in the car, and in any condition (though the police might get jumpy if they see it). Until Brady/NICS, there was only the "yellow form" - no background check, no waiting period. There is still no backgrouond check required for private transfers.