Did Shimano make a TT brake/shifter for the 10sp Ultegra di2 (6770)? Can’t find any evidence of it?
no. people use the DA version or no brake/shift combo …to save money
now they do make Ultegra (11speed) - has aluminum brake lever. DA has the carbon levers - not sure if backwards compatible.
read about compatibility: http://carltonbale.com/shimano-di2-everything-you-need-to-know/
The ST-6871 is fully compatible with 6770 mechs.
http://bike.shimano.com/content/sac-bike/en/home/components1/road/ultegra-di2/st-6871.html