Harry,
As stated, new seals will help. Check your pistons to see if they're heavily corroded...if they are, then replacements like Lumpy suggested are the best way to go. Pattern ones from Nikone or similar work fine, used them regularly on my own brakes, not too sure about less familiar names....
Nikone FZS rear brake seals - ebay item # 190572911422
Fazer101 - excellent update to the knowledge database....I suggested last year that the Thunderace / YZF750 / early XJR1200 rear calipers *might* fit as they looked the same as the TRX850 one, nice to know that another rear caliper definitely fits. Beats me why Yam didnt fit those calipers to the FZS600 in the 1st place....