The only restrictions I can find, where a gun is required to be "securely encased", or "not readily accessible for immediate use" only apply to concealed weapons. In a vehicle or otherwise. So, if your handgun is concealed and you have no permit, it has to be in a case or inaccessible. You cannot have any loaded weapon in a vehicle without a permit. "In a gun rack" would fit the criteria of being not readily accessible, but if it's not concealed then it shouldn't matter. I am citing Utah Code 76-10-504.
I have been checked by CO's while driving on a hunting trip, with my hunting rifle on my lap, and a full magazine (action open, nothing in the chamber). They told me it was legal to do that, as long as there was nothing in the chamber.
So, my personal understanding is that a weapon has to be in plain sight, or, if it is concealed, then it must be securely encased or not readily accessible for immediate use. Neither of those apply to concealed permit holders, however. They are exempt from the "loaded firearm in a vehicle", and also concealed firearm laws.
There is nothing that prohibits having ammo with the gun, or even in the gun when it is cased. The gun just cannot be "loaded", which means nothing in the chamber for a rifle or semi-auto pistol, nothing under the hammer for a S/A revolver, and nothing under the hammer OR in the next chamber for a D/A revolver.