On mine, there are two hoses, one from the xfer case and one from the transmission. These are joined with a T and then the free end is just zip tied to another cable up near the starter. They don't connect to anything really.
Their purpose is to serve as a vent for the transmission and xfer case. As things heat up, the air inside the gear box expands and the hose lets that air escape -without putting pressure on the seals. Also, just as important, when you suddenly cross a stream full of cold water, the air inside will contract and the hose lets outside air in -without sucking dirty water past the seals. Dirty water inside the axle, transmission, or xfer case is not good for the gears and bearings.
Some guys put a little fuel filter on the end of the hose, just to keep dirt out. Ideally, you keep the end of the hose up high enough so that even on deep water crossing you don't get water into the gearboxes.
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MarkB.NV
1991 Tracker, 8valve 1.6L, 5 spd, 4x4, 2 door, soft-top, 103,xxx miles, w/ 2 in suspension 2 in body lift, 30x9.5/15 MT tires.
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