The fuse panel is under the "d" panel, which is the black panel under the left grip, below the glove box. Here's a link to the owners manual. Follow the manual to get the panels off or things will break. Good luck!

http://www.yamahamotorsports.com/assets/service/manuals/2008/LIT-11626-21-63_FJR1300A_1543.pdf

 

fuse box

The only thing under that panel is the radiator filler and the horn.
At least that is all I could find this afternoon. Mine is a 03' and does not have any box on either side. The right side is the battery..
Thanks for the information on the manual.

 

Try this one says for 2001.

http://sabmag.dougc.com/downloads/FJR%201300%20Owners%20Manual.pdf

 

According to aide's link, the fuses are under Panel D. That is inside lower right panel next to the fuel tank.

 

fuse panel

Found it just behind the battery!!!!

 

Are you sure it's an FJR?

If you've found the cooling system filler, then you've opened the panel that the fuses are supposed to live under. On the right hand side there is normally only a single large 50amp one that is attached to the front of the battery cage, and a blade type starter circuit fuse which lives on top of the starter relay, along with a spare.

The fuse boxes on the left hold someting like a dozen mini blade fuses, and the top one slots into a dovetail arrangement on the underside of the black inner fairing panel which you have already taken out, just in front of the hazard light switch.
If a PO had failed to put it back in the slot, then it might have slumped down between the other fairing panels, which is why you haven't found it yet.

Mind you, it's always possible that the PO had done some major rearrangement to the wiring loom.