Hi it's all hydraulic dont seem to be any electrical componentNot many tractors over here have trailer brakes, they are starting to appear some on the larger tractors.
You don't say if they are air or hydraulic, if air pressure and the electric valve.
I had a few minutes so I went to Messicks NH web pages and looked up parts for a 7810,
they have about six different pages of pictures and brake componets.
The NH website should have the parts breakdown and pic's also.
New Holland (781) - 6 CYL AG TRACTOR (1/89-1/91) Parts Diagrams
What did I miss?
I did not see anything on the referenced web pages that referred to TRAILER BRAKES.
I can see diagram of parts only think they dont say which part is what number but usefull diagrams