[KTMasean]

I am not familiar with the steel tank Dukes.
Have you had this bike since new and if so was it leaking always?
If not leaking always, what has been done to the tank or filler cap to have it start leaking?
I think, as with the first-gen Dukes the overflow only releases fuel if at filling up the fuel spills over into the filler caps ring reservoir. (this also drains the rainwater)
If yours keeps dripping this means (probably) that the filler cap doesn't seal well.
Check the cap seal first.
Good luck.

 

[KTMasean]

As said I have no experience other than first-gen Dukes (ridden a few 2nd Gen ones but have not worked on them).
I would try to take off the filler cap (I learned on the 2nd-gen it is all 7 screws while on the 1st only 3).
Check the seal between tank and cap.
You may even find that the 7 screws and not tight enough, check torque specs.
Good luck and keep us posted