UPDATE: I'm a moron!!

It turns out that that hose is meaningless and just acts as a "vent hose" as some people have called it. I went and checked every connection in my engine compartment after I installed the new engine and it ended up being a loose connection between the hard plastic vacuum line that goes to the brake booster, and the vacuum pump. The car operates splendidly now. Thanks to all who were concerned enough to read this thread.

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1981 240D/297K/4-spd/OM617 (mine)
1982 240D/241K/4-spd (wife's)
1979 240D/291K/4-spd/OM617 (father-in-law's)
1983 300DT/240K/4-spd (brother-in-law's)
1985 300DT/???K/5-spd Intercooler conversion (brother-in-law's)
1985 280TE/160K/5-spd (father-in-law's)
1963 UNIMOG (brother-in-law's)