sad·dle
   [sad-l] Show IPA noun, verb, -dled, -dling.
noun
1.
a seat for a rider on the back of a horse or other animal.
2.
a similar seat on a bicycle, tractor, etc.
3.
a part of a harness laid across the back of an animal and girded under the belly, to which the terrets and checkhook are attached.
4.
something resembling a saddle in shape, position, or function.
5.
the part of the back of an animal where a saddle is placed.
har·ness
   [hahr-nis] Show IPA
noun
1.
the combination of straps, bands, and other parts forming the working gear of a draft animal. Compare yoke1 ( def. 1 ) .
2.
(on a loom) the frame containing heddles through which the warp is drawn and which, in combination with another such frame or other frames, forms the shed and determines the woven pattern.
3.
the equipment, as straps, bolts, or gears, by which a large bell is mounted and rung.
4.
Electricity . wiring harness.
5.
armor for persons or horses.
After reading these I would probably say harness. Saddle has that animal feel to it. I have used the terms interchangeably. If it's for ease of reading I would probably just meet in the middle and go with "harness/saddle" just to cover the basis.
Also it's gravy. I'm a convert to it but I do still love my brown gravy. Don't ever bring that conversation up at thanksgiving dinner with a bunch of Italians, your going to loose the debate.