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It's cheap enough to replace the line, and depending on where you live you most likely need it. The line connects behind the glove box, drop it out of the way and find the white hose going through the firewall, pull out of the connector and replace with your new one.
You really shouldn't splice the vacuum lines, replace the whole thing. It will hold for a time but every splice I've ever seen has failed, and like he said it's cheap so why not spend the extra $2 and run it all of the way? It's lazy repairs like splicing instead of replacing that give the next owner headaches for years to come.
What does the vacuum motor do exactly? does it have to do with re-circulate? I'm surprised to find very little information about it on Google. Just curious.
It's actual name is "Blend air door actuator", it controls fresh air intake into the HVAC system. Using vacuum it can close/open fresh air port for max a/c and defrost modes, switch to window/floor/vent tubing as well as controls air flow over the heater core fins.
A properly functioning BAD actuator will move when the climate control **** is moved from Max AC to Vent as well as from floor to either defrost mode.