Welcome to the forum gsxr1100 (nice bike by the way)
Have you had the back light clusters out to check for signs of any corrosion on the fitting/ twiddle the bulbs and connecting wire light block about while the lights are on to see if you can clear the fault?
could be a bad earth somewhere on the circuit ?
If you cant resolve it by doing any of the above might be worth getting it down to a local Auto electricain with testing equipment etc who should be able to sort it out.
Good luck with fixing it and let us know what you find .
Cheers T-sport