I've heard about those mounting contraptions but never saw one. I could tell a few stories about how individual stallions liked everything a certain way that would keep lay people in stitches but being its a family board and I wouldn't want to get banned ... Horses are amazing and intelligent creatures and they are as individual as humans.
Friend of mine had a QH stallion who would not treat it as "just business" - he had to fall in love first. They usually put him and the lady of the moment in adjoining paddocks (with an access road in between) so that they could get acquainted. I'm surprised they didn't have a "perfesser" out there playing mood music on the bordello piano . . .