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given the length & location of the hose, i'd vote "no way jose'" that it's an unused battery vent line. very much wrong location, tho diameter looks about right.
Actually, it looks about as long as mine did before I removed it after replacing the regular battery with a gel cell. It had to be long enough to go up to the top of the battery on the left side of the bike. It's too long to connect to one of the vent line "mid-connectors" and too short to reach the fuel pump access plate on the tank. So, I don't think it's a fuel vent line. Again, the diameter is typical of the battery vent.
so Rob- it's one week later from your original post. What did you find?
yes, but that vent is on the right side of the bike, not the left. (battery location on my 11S is behind the tank, under the nose of the seat- the "classic" BMW battery position- so the apparent position of this one is very wrong from my perspective.)
If I recall correctly, on both my 1150RT and my 1150R, the battery vent hose went from the left upper edge of the battery where the vent is located, down the left side of the battery, across the bike to the right side behind the battery, and ended behind the right brake petal with all the other vent hoses. When pulled out from the battery tray and extended along the right side of the bike, the length is as pictured. It seems more likely to me that a previous owner would leave a battery vent hose unattached after switching battery types than to leave a tank vent hose disconnected. The original poster can look on his bike and see if there is a battery vent hose, two tank vent hoses, and two overflow hoses from the ABS pump, if so equipped.