does both bases of this characters base need to be occupying hindering terrain to activate stealth?

The half of the dial your opponent is drawing line of fire to has to cross hindering or be in hindering to use stealth.

yes they have to occupy hindering with both bases, or at least LOF has to pass through hindering to both bases for stealth to activate

and

So, in order to gain the benefit of hindering terrain, the line of fire must cross hindering terrain. ONLY the half that is in hindering terrain gains the benefit. So, if you can draw Line of Fire to one side, but not the other, then the Stealth won't work. On the other hand, if you can only draw line of fire to one side and that side is in the Hindering Terrain, then the Stealth does work. Though, I can only think of a few situations where only one side would be 'visable' but not the other....

Just quoting the books to emphasize what was said.

k thanks a lot.

Blocking terrain or another character covering the half that isn't in hindering, or that half simply being outside of their range come to mind.

Occupying hindering terrain does not "Activate" stealth. Lines of fire activate stealth. More specifically, a line of fire that passes through hindering terrain activates stealth. It happens that the square you occupy counts for this as well, but it's still the line of fire causing stealth to activate, not occupying hindering terrain.

ON the graveyard map, if my character in in the open grave terrain, can I draw line of fire to shoot other characters?

Sure. LOF drawn to the character is blocked... but that's it.

meaning, as always, any stealther could be sitting wide out in the open and benefit from stealth- so long a the Line of Fire crosses through Hindering Terrain ANYWHERE along the way (Which does not include the square the attack is coming from)

What if only half of a Peanut Base is in the grave, can you draw line of fire to the part of the base that isn't in the grave?