The other end connects to a pipe on the base of your air cleaner with a small section of hose. Clean air is drawn from there through the exhaust manifold pipe (if it hasnt rusted away) and then into the choke actuator on your manifold.

You can get electric thermostat conversions for the choke, if the manifold heater is no good or your thermostat coil is not working (the thing on the manifold).

The front vacuum break (pull off) acts on the choke it will open the choke slightly against the thermostat when the engine starts to allow some air flow, depending on throttle position, and you are correct it also closes the secondary air valves.
When the choke is at the off position the vacuum break is still part of the secondary system, it helps to regulate the air valve at transitional throttle and engine loads (vacuum).
As Dr Terry says air pressure difference above and below the air valves opens the secondaries against a spring, but this will only happen if the vacuum break is released (low vacuum at the diaphragm).

Make sure you test it, you can see it operate easily with the air filter off. Check its operation by observing it when the car starts, it should pull on very quickly when the engine starts and is at idle speed, pull the vac hose off of it and it should pop straight out. (engine might stall from the vac leak)

If it is not working make sure you get a new one before you do much driving otherwise you will have problems with choke operation and bogging down when accelerating (because the secondary valves will open prematurely or pulse slightly).

P.S. Don't worry if you can't see it release by revving the engine in the shed, it is designed to release at very specific vacuum setting (has its own internal spring and release valve) you probably will not be able to do this in the shed.