Go to
http://www.corvette-101.com/vacuum.htm for a diagram and a how to.
You probably cross-connected something, or cracked a post on a vacum switch or something when you removed the old units.
As stated above, you should normally have the engine running when ever you're opening and closing the headlights. Leaks in the system will cause them to "pop" up sometimes after you shut the engine off.
A tight vacuum system doesn't take very long to close at all. A leaky one could take all day!
Also check the manual overide switch located just inside the dash under the steering column. It's a push-pull switch which operates in the vertical plane. Pull it out (down towards the floor) to open the headlights without using the normal headlight switch, (headlights pop-up, but the lamps don't light) and push in to return to the normal closed position.
Check the position of this switch, it might be why everything seems to be working inversely, but if its a new-to-you-Vette, there's probably a leak somewhere.
I got so tired of vacuum leaks over the years

, that after I had replaced all the vacuum hoses, actuators, etc. I installed a vacuum gauge just under the dash on the center console, just so I could keep an eye on the manifiold vacuum and check for leaks while driving.