Before you go off on a rabbit trail lets get back to when you found the issue. You mentioned that the bike runs fine with the seat off, an not start with it on. Your problem lies there. In order for us to be able to better help you we'll need to see pictures of the area from all kinds of angles(from just about any angle from above at a 45 degree. Would help to remove your tail fairing as well.
From what you have described i betting there is a wire routing issue that should be a relatively easy fix. We'll also need to see how the bottom of the seat interacts with the sub frame.....you'll want to put the seat in place and slightly pick up the rear and snap a few shot from the side as you pull up the rear edge of the seat. An easy way to see if you have any interference is to put a thin layer of grease on the underside of the seat. Bolt it down and sit on the bike. Squiggle around to see if you can get any part of the seat to mash down into something in the subframe. Pull the seat and see if any grease is left on anything in the subframe. You can use a very thin coating of a bearing grease, or something that is thick enough to be spread out and not drip. Only takes a very thin layer, and wipe up is easy enough.
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