Any instructions with the LED to say which is power and ground?
If not I might guess that the white is ground and the other three power but on LED, that may have to be tried andswapped if not right. Polarity is needed on LED and many do not use any "standard" as far as I can tell!
For where to tie to power and ground, how do you want this to work?
I see two different build dates for your RV, early and later in the year and one difference seems to be an awning light switch.
Do you have that switch and would you want the grab bar tied to come on with the awning light or prefer adding a new switch to control it seperately?
There appears to be a blank switch plate next to the awning light switch and that would seem to be a place I might put a new switch to match the existing???
Or there is also a porch light switch shown and that could let you make the proch and grab bar work together?
Wire JF seems to be the power wire on both of those but with LED, the current draw will likely be so small it can piggy back with most any of the 12 vdc in that cabinet without preesing the fuse much.
For ground, any place where you can find it will work for the grab bar.
Click this drawing to get a better view!