Hi guys. Just finished replacing the waterpump in my '95 E320. (I'll post my 'experience' with that project later

as I ran into a few difficulties, like the tensioner bolt stripping during the dissasembly ///// and the dealer gave me a timing belt that was too big - took awhile to figure that one out - SO make sure you compare timing belt sizes). Fortunately, all is back together and the car is running fine.
But I checked the operation of my heater, and it's not working. At any engine speed, at any setting of the ACC. The engine is definitely running warm enough for the heater to kick on, as she idled in the driveway for about 30 minutes tonight as I was checking the operation of the waterpump.
My main question is around this hard, plastic "white" vaccum hose that attaches (sorry for the failure terminology here, I'm totally guessing on this part) just under the front RH side {passenger side} of the valve cover - there's a control module here - a smaller black box - and this white vaccum hose travels from this module under the intake manifold to another fitting.
During my waterpump replacement, this hose snapped like a piece of uncooked spaghetti. And I'm wondering if this broken vacuum line is the cause? I think the heater was working six months ago (in texas, haven't used the heater since March).
Can anyone tell me what this white, plastic vaccum line does? Or what it's called? I'll try to get another from my dealer asap.
If this doesn't solve the problem, I'll start investigating in all the other options, like a mono valve replacement.
Many thanks guys for your help. Best regards, 71Rcode