Those 'horse blanket' style seat covers generally have a rifle pouch located along the front of them under your legs. Maybe that's not your style, though.
I carry my Scattergun behind my trucks' rear seat (it's a crewcab) and, I'm sure, the area behind that is close in size to the area behind your reg. cab seat. I use an old soft gun case that I leave unzipped and oriented up so that all I have to do is lean the seat forward and there's my baby!!
If you're going to store a shotgun this way you should routinely remove it for a good cleaning even if it isn't fired often. I usually fire mine most every weekend but have left it back there for extended periods without looking at it. I keep a pretty clean truck but find that after a month or so the gun is covered in lint and other minor garbage.
Also, scenarios where you would deploy such a weapon for your or another persons' defense generally mean longer engaging distances. Consequently, you should, and I do, only load slugs in such a gun. Keep the buck in a sidesaddle or ready belt. Slugs will do fine up close and excel at the longer (over 15 yards) ranges along with keeping collateral damage to a minimun as long as you hit your target.
As with any defensive firearm, practice your ass off!!! Have fun.
CB