Martin,
You've really done a lot and it's looking Good!!!!
As far as that bracket goes, (and this is only guessing) it looks like some kind of electronics mounting box.
And, from your other pictures, it looks like it did fit under the seat so it could not have been very big whatever it was.
The rolled over ends kind of look like whatever was in there slides in from the left side and latches shut?
?
Could it have been maybe something like the replacement electronic switch unit (M Unit thing?)
Or maybe an electronic ignition unit???
Can you get a better picture (not as dark) of that bracket, maybe top and sides?
I'm inclined to believe that it might have been something off a Police Bike?
?
Really nice job so far.
Charlie