97 Astro vacuum lines

All...I realize that this subject has been touched on numerous times...hopefully I will be able to explain what I am looking for. My ac/vent/heat damper controls are not working. I traced the vacuum line through firewall to a multiport elbow type connection. Looks like one connection is 1/4" vacuum line from a globe shaped object on passenger side of of vehicle (possibly vacuum reservior?). The other line looks like 1/8" plastic tube (or really cheap vacuum line?). This 1/8" tube is broken....Any idea where this goes? I haven't been able to figure out where this goes. One more thing, I checked with the local autoparts store (autozone) and they don't carry 1/8" vacuum tube? Should I try to sleeve the existing tube with 1/4" tube? Any opinions or additional detailed info would be appreciated. Thanks.

Ignore my earlier confusion. I found the two ends of the 1/8" tube. I sleeved them with 7/64" rubber vacuum line.

Ignore my earlier confusion. I found the two ends of the 1/8" tube. I sleeved them with 7/64" rubber vacuum line.
Where??? I can't find the other end.

For the next poor sod with this problem, it's found from inside the car looking at the throttle body about 5 inches from the throttle body around 7 'O-clock position.