Reading through, it's not clear but I'm assuming that the back rest is not OEM but is aftermarket, that you don't know the make, but that you do know that there is a bolt-on rack for it (based on a diagram you have).
Correct? If I'm not, then we need some more info in order to help you out.
In any event, can you take a pic of the backrest and post it here? Then folks can see if they recognise the make? You can do that by storing the pic on one of those picture hosting websites (or if you have an album on this site already - put it there). Then create a link to it in this thread by adding a post, clicking on the URL button below, pasting the link in the pop-up and adding some text to prompt us to "click here"