I installed a proportional braking system - purchased all parts and did the install myself.
That's base plate, tow bar, electronics, etc.
To do the work properly EVERYTHING must be secured and protected - as good as or better than factory wiring.
I estimated my labor would have been around $1000. for the install.
Parts were in addition.
I would not let some kid or shade tree mechanic do this work.
That said, I think your quoted price is too high. They must be tripling the price on parts and adding labor too it.
I would look for a parts and labor price of closer to $3,000+ Under $4K for sure.