Going on memory from a decade ago, but the '59 Fury I almost snagged had the under dash dealer A/C - black, rounded corners and round white vents on the front and sides.
Does your exploded view pic look anything like that?
No, In the 59 parts book page 24AG it shows a Model D system, it is a large rectangular unit with square edges and three large round registers in the front, none on the sides.
Dick.