Yep, there are several potential leak paths with these things. Things like a loose rivet can be especially insidious.
Fill with water and see where it's coming from. Turn it upside-down to check the lid seal. Hang on the bike to put stress on the mounting points.
You might need to use RTV, have a cracked seam rewelded, bash a few rivets to tighten them up, enhance the lid seals somehow, or all the above.
2002 Suzuki DL1000 V-Strom, Dark Metallic Space Blue
1983 Suzuki GS850G, Cosmic Blue
2005 KLR685, Aztec Red - Turd II.2, the ReReTurdening