If I recall correctly, the last fuel indication bar starts flashing with roughly 4.5L remaining in the fuel tank. The fuel symbol joins it by flashing at 3L. Both remain on flashing until empty.
It's generally not a good idea to run the tank empty since the fuel cools the pump.... no fuel equates to a hot fuel pump motor. If you do have to ride the fuel tank until empty, as soon as it stumbles, shut 'er down.
Another point, is that there are many reports on google, of riders having ridden their V-Stroms to the point where they have run out of fuel and have then discovered that their fuel tank was not completely empty. When they refilled the fuel tank, they where surprised that by the amount of fuel that it took to completely fill the tank vs the fuel tank fuel capacity.
I found that often after the bike has been stored for a while with a less than full fuel tank, that the top block on the fuel gauge didn't show up after I filled the tank. This is due to the fuel gauge level, that works on a resistive wiper system, not making proper contact for some reason. Many have posted their cures for this. I find it easier to make use of one of the trip meters to monitor the fuel range of that fuel tank.