Ok, thanks for the feedback, I'll try to see if we can find the point where you begin to lose understanding. Hopefully, I didn't screw up the link below.
DX-1000 & IC Controls ASC3000
No non-derail for the moment, let's just discuss the switch connections. I'll try to be more careful with my terminology. Can you see from that diagram where the two wires from the voltage source are? One is labeled COMM and one is labeled 12 - 20 vac. Just cover the DZ-1002 on the right side with your hand. You don't have the stuff on the right past those black dots so just ignore it.
You're going to wire one side of your power supply to the middle wire on the DZ-1000 switch machine on the left. You're going to wire the other wire from your power supply to the COMM on the ASC. Then you connect the switch wire labeled R to either 1 or 2 on the ACS, and connect the switch wire labeled L to the last connection, 2 or 1.
How the switch works is that there is always voltage at the middle wire, but the circuit is open because there is no connection back to COMM, the other side of the power supply. The path from the switch back to the COMM is through either the left wire or the right wire, depending on how you operate the ASC. The two relay connections on the ASC, 1 and 2 that connect with R and L, will provide the connection to COMM when you select straight or diverge. Then a path is established between the two power supply wires, 12 - 20 vac and COMM, and current flows, the switch throws and every body happy.
How are you doing to this point?