on bed mounted plug in....anything you can do to make hook up easier, I'd say go for. you're already going to be climbing around to hook up chains, etc!

I dont know where you will park store or take your trailer but here in UrbanPonyLand, a locking battery box is a must. those batteries walk away ALL the time. Mine is under the gooseneck as you described.

good luck!

The plug is strictly a personal preferance.  If you have one inside the bed.  You never worry about excess wire dragging on the road.  But you will probably have to open the tail gate to plug and unplug it. ( unless you have long arms and are tall and can reach over the bed side rails.

I had one GN with a single battery that was used only for inside lights and it worked fine,  If you want any heavier electric consumption, Then two will be needed.

I've never had a battery walk off in 17 years of using GN horse trailers.  So that risk will depend on where you live and honesty of the people in the area.  Mine sit on a simple tray under the Gooseneck and above my spare tire, Neither are locked or secured.