The "vacuum" line is only to allow a failed regulator to vent gasoline back into the breather hose instead of leaking externally, possibly causing a fire. It may have no impact on cold starting but should be replaced regardless. Also check to see if it has contaminated the oil with fuel. Sniff the dipstick, if you can smell any hint of gasoline change the oil.

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90 300TE 4-M
Turbo 103, T3/T04E 50 trim
T04B cover .60 AR
Stage 3 turbine .63 AR
A2W I/C, 40 LB/HR
MS2E, 60-2 Direct Coil Control
3" Exh, AEM W/B O2
Underdrive Alt. and P/S Pulleys,
Vented Rear Discs, .034 Booster.
3.07 diffs 1st Gear Start

90 300CE 104.980
Milled & ported head, 10.3:1 compression
197° intake cam w/20° advancer
Tuned CIS ECU
4° ignition advance
PCS TCM2000, built 722.6
600W networked suction fan
Sportline sway bars
V8 rear subframe, Quaife ATB 3.06 diff