One simple rule of thumb. Out of sight out of mind. There are some pretty sad stories about guys coming out of their hotel rooms halfway home and finding out they no longer have an elk rack.
If I have a cap on the truck, they will be the first thing to go in the front of the truck bed. If not, they go in the enclosed trailer.
Always good to avoid lengthy game checks as well. If you want to show your elk antlers to the world, do it when you get home.