A 63 shop manual is a must for you to own and browse through. Page 13-18 if you have one. They are readily available in ebay.
In the help tab, scroll to the vacuum diagrams.
Vacuum Schematics are posted on our Help Page under Vacuum Schematics and Pictures Scroll to 2nd page in the photo album, then go down 4 rows and click on diagram on the left. Click Here for a direct link. If you don't have a shop manual, it is a must, and I have a VG used original for $40 + s/h. Shoot me an email to email@example.com with address if you need one.
The manifold vacuum fitting is missing a line that goes to the electrical connector block on the fire wall. That vacuum line is what feeds the vacuum to the heat/AC system.
Is there a color stripe on the loose hose? If there is no color stripe that can be seen from the engine compartment(e.g. it has been replaced with a newer hose) , you need to get under the dash to see what it connects to? Otherwise we are just purely guessing. If you see it has say a specific color stripe and looks like an original hose, then it is a safe bet it is connected correctly on the inside of the firewall, and you can use the shop manual to determine what it connects to in the engine compartment. If you want to make absolutely sure, especially with a car that has obviously had vacuum lines chopped up, I would still get under the dash and trace hoses.
Taking a quick look at your photo, it looks like I see a hose running to your water control valve. It would be a yellow stripe if factory hose. It also looks like perhaps you have one running to the Fast Idle control valve (blue striped). But it is hard to say, as I do not see the color of the stripes, and of course in 50+ years it is easy for anyone to just unplug a hose from one component and plug it to something else... simply because the hose reaches!
Also keep in mind that a problem with posting actual pictures is I would say 90% of the cars I have brought in, running and non-running, and every driver car, has hoses either disconnected or running to the wrong component. For most cars, hoses get disconnected, switched around, and replaced with 50+ years of maintenance.
So if you or anyone is looking for reference to correct hose hook-up, the diagram below is the best way to start the process. It shows hoses from component to component as it was assembled from the factory.
IF...and that is a very big IF, you want actual pictures you need to preface the question and ask "Does anyone have actual pictures of all the vacuum lines that are connected 100% correctly?" I can easily show you a 1/2 doesn't 63 engine compartments with INCORRECT vacuum lines. If someone has went through the process and validated everything is 100% on their 63 (or 64) that would be fantastic. I would still probably be a bit anal and want to go back to the shop manual and validate everything, just to make absolutely sure it is 100% correct. Putting together an album with all the intricate details of every vacuum line is on my to do list (if no one gets to it first), so we have actual pictures to go along with the vacuum schematics.