Ok, so nobody knows the answer. After a lot of asking around online I still couldn't find anyone who knows what size these should be. Well I can clear this up myself and it may help some other poor soul who comes across the info.
With a bit of work with a micrometer I got the outside diameter, (8.8mm), and the thread pitch, (close to 2.35mm for 3 threads). That seemed to put it into the M9 x 0.75mm category. Looking at the thread specs that fits exactly with a M9 fine thread which is available. I had to dig around a bit but sourced these from an ebay seller who wasn't asking for my dog and daughter's hand for 2 nuts. Don't go for anything "Boss Replacement". As soon as the Boss name or the idea of a pedal or guitar is attached the price rockets. Just buy a common or garden "M9 x 0.75mm" Half Nut (or Jam Nut) from a fastenings supplier. The half nut marks it as the slimmer type, (only 2mm thick), which we need for the Japanese pedal and guitar sockets. These nuts are commonly used to tighten against a full nut so it is locked or "jammed" into place.
I have attached a picture of the two nuts which are originals and the new one fitted. You can't tell the difference and the thread is a perfect fit. I don't have the washer in place yet but it is sitting at home base waiting so the pedal will soon be back to exactly original spec as you can see.
So there it is. Boss pedals need M9 x 0.75mm half nuts.
With a bit of work with a micrometer I got the outside diameter, (8.8mm), and the thread pitch, (close to 2.35mm for 3 threads). That seemed to put it into the M9 x 0.75mm category. Looking at the thread specs that fits exactly with a M9 fine thread which is available. I had to dig around a bit but sourced these from an ebay seller who wasn't asking for my dog and daughter's hand for 2 nuts. Don't go for anything "Boss Replacement". As soon as the Boss name or the idea of a pedal or guitar is attached the price rockets. Just buy a common or garden "M9 x 0.75mm" Half Nut (or Jam Nut) from a fastenings supplier. The half nut marks it as the slimmer type, (only 2mm thick), which we need for the Japanese pedal and guitar sockets. These nuts are commonly used to tighten against a full nut so it is locked or "jammed" into place.
I have attached a picture of the two nuts which are originals and the new one fitted. You can't tell the difference and the thread is a perfect fit. I don't have the washer in place yet but it is sitting at home base waiting so the pedal will soon be back to exactly original spec as you can see.
So there it is. Boss pedals need M9 x 0.75mm half nuts.