Fork oil leak is the most common but you said you checked. Spots under the fairing, I assume, rather than the wheel/forks?
On my 2007, the radiator overflow reservoir became very brittle and cracked causing a leak. I have heard of this happening on a few bikes - relatively cheap to replace... I did a "patch" with a product called Seal-All plus some fibreglas cloth but tank was too brittle to trust it for long. Temporary for a week until dealer could order the reservoir.
I also had an issue with an actual radiator leak. Back side near the top left and not the result of inept maintenance or a rock - just happened. I was able to get a radiator shop to fix it - they injected some sort of rubberized sealant which blocked off the one affected tube. I think it would be tough to braze that radiator!
If the leak is water soluble, it could be brake fluid or antifreeze. If not, consider fork oil or engine oil. Odor can help identify.
This was my radiator thread
https://www.fjrforum.com/threads/leaking-radiator.172405/
Good luck.