restoring 1990 5th ave. Need help, please!

HEAT/AIR: (Thermostate controlled)
There are two vaccuum tubes coming from behind the dashboard though the fire wall. The Yellow one is connected to the Master Cylinder Vaccuum line. The black one goes no where. So, what is it supposed to hook to?
Also, the relay switches at the other end of the tubes are constantly clicking even when the heat/air is shut off. I can't get any heat out of the system at all.

TRANSMISSION: (automatic front wheel drive)
The tranny slips out of gear (as if in neutral) shortly after taking off. It only does it once during a trip.
It will not shift into 3rd gear at all.

Thank you for your help.

The second HVAC vacuum hose probably goes to a heater control valve in line with the heater hose to the heater core. I'm not sure what you mean by the "relay switches."

The transmission issues you are experiencing sound a lot like the common issues with the Chrysler autos of that era, similar to those used in their minivans. Lots of information available about those on the Internet, so I won't re-post that info here.

-Rod

Welcome to AF.
The transmission in your car is an early version of the 'Ultradrive' model and it's reliability is a HUGE issue.
Look here for more info:
http://www.autosafety.org/chrysler-ultradrive

Also Wikipedia has some handy general info, too:
http://en.wikipedia.org/wiki/Ultradrive