Maybe SRAM Eagle to Shimano 12 is the not needed
From the Sheldon Brown link:
Indexed rear-shifting systems from
Shimano,
SRAM, Campagnolo and SunTour have different amounts of
- cable travel per click,
- derailer movement for a given amount of cable travel, and
- sprocket-to-sprocket spacing.
I took that to mean that you will have to have some kind of adapter/translator to get them to play together.
I'd be interested to know what you find out.