Update:
Yes. The 2 amp does work. The secret is to remove the keys (OK, key fob) and let the truck go to sleep.
I put the battery monitor on yesterday and have been watching it with and without the charger.
Today I let the truck go "asleep", hooked up the 2a charger at 15:28hrs. By 18:04hrs it was fully charged.
It went to low because I was installing and playing with my new lights.
Having said that. Fordpass has given me the dreaded "shut down to save battery" message before. But it has always started. maybe I was worried about nothing?