Where does the 5 vacuum lines go on the ac heart switch?

The simple answer is as follows:

The first (red) and fourth (blue) are directly connected to the flux capacitor in the ML-29C Recipator. The second (green) is power distributing line, and connects to one of the 4 LAC sockets on the top right side. The third (brown) is a back-up power line, but is usually not active. It is also connected to one of the 4 LAC sockets and becomes active if the green line fails for 5 aggregate seconds on a 12 second timer. The fifth line (larger black one) pumps the lubricant oil throughout the device.