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Using my 02 manual I couldn't find a definitive statement that says what it is exactly for.
I did find a note in the removal/replacement procedure for the vent hose that says to "observe the orientation of the transmission vent hose check valve prior to removal of the hose."
Upon installation, "orient the transmission vent hose check valve as noted during prior to removal". Not much help I know.
I bet if you look at the vent in the end of that line it's a Tabs valve.
What that is, is a 1 way valve that allows heated air to escape but it closes when it's drawn against to prevent water intrusion into the transmission.
What the part T'd into the line is, is a restricter to allow a slow return of cool air back into the transmission. :crazy:
Your axle vent is a Tabs valve also, I thought I had a pluged vent on my axle untill I blew some air into it and heard the valve unseat itself. :D