Eisbein, is there an easy way to get to that float bowl to open and drain it? I had a look last night but couldn't see a way to quickly get at the float bowl.
Then, if it is water in that little bowl, is it OK to ride the bike like that even if it splutters? Will the water just work itself out of the system?
And how on earth does water get in there in the first place?
I don't know on the Djebel, but there should be (at the bottom of the bowl) some form of extruded point with a bolt or screw (can be an sunken or normal screw/bolt).
Similar to the bottom (please note that the red circle is the one I added highlighting the drain - the black line was there from another article on where to adjust).
It may or may not have what looks like a 'bleed nipple' with (or without) an overflow pipe attached to it.
If I remember correctly you don't take that screw/bolt out totally - you just turn it out 'till fuel begin flowing out of the bleed nipple.
Just make sure that you know how the petcock (tap) works. On some bikes you have a 'prime' as well as the normal on/off/reserve setting.
If you drain the float bowl and you don't have a 'prime' to fill it up again it will crank a couple of times before it will start as it have to fill the bowl with fuel again.
The standard disclaimer of 'if you are wondering about these things then it is probably better to take it to someone who has done this before' applies.

Also - having said all of the above - have you checked out the side stand switch as well ?
Friend of mine had it on his KLR that the bigger vibrations of higher revs caused the side stand switch to become very finicky and cause the same type of symptoms.