Where is the other end attached? The brown lines are usually for the "shut-off" function (not climate control or A/C, these are green). I presume your car shuts-off or you would have said so. This makes me wonder if some lines have been switched. There should be a black line coming inside and going nowhere. It is the vent for the proportioning valve (goes inside to pull clean air) mounted on the back of the injection pump. Of the two lines attached to the proportioning valve the one that goes inside the dash is the one that comes out the side horizontally.

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Steve Brotherton
Owner 24 bay BSC
Bosch Master, ASE master L1
26 years MB technician