Thank you for the help. It is a 63 and sounds like connecting the hoses may solve any issues?
Dave, Your 63 does not have a Comfort Control System or Thermal Vacuum Valve so you can ignore the prior replies regarding the 64 system.
That is the Water Control Valve in your diagram circled. It allows hot water to enter the heater core when in "heat" mode, and blocks hot water from entering when heater not on. You can see it in the 1963 Shop Manual on page 13-1, Fig 13-1.
Your Picture is low res and I cannot tell where the other end of the vacuum hoses originate or the color striping on them which is key to using the 1963 Cadillac Shop Manual to understand where they connect. I am also not sure if this is an AC equipped car or non-AC. That will make a big difference. You can see the vacuum line set-up for Non-AC cars in the shop manual on Page 13-2, Fig 13-3; and for AC equipped cars on page 13-18, Fig 13-16.
If you do not have a shop manual that should be your very next purchase as it will answer many of these basic questions. If you don't have a shop manual you can find repros in print and cd, and originals on eBay, Etc. I have an excellent original 1963 Shop Manual for $60 ($45 as a Chapter Member).