It is either air entering the system, due to porous flex hoses (not very likely) or a soft mounting, using thin flexible metal, of the master cylinder.
VW had this problem with their type 4 back in the 70s...This entire car was a problem( 4 year production run)...
But the Lincoln LS is different than an Edge- the same design, using thin metal, is not likely...
Maybe this is a quirky master cylinder design ???