Thank you all for the replies. It turns out that I accidentally omitted a line from my diagram. My car DOES have a line running from the radiator directly to the expansion tank.
I am still puzzled by the T junctions that are set into the lines to and from the heater core that also go to the expansion tank. It sounds like those are not needed. I wonder what the intention was in running them...
I have added two additional photos that show more or less the complete system.
Not shown are the fact that the radiator inlet and outlet fittings are at the top and bottom on the same side of the radiator, I guess that means this is an aftermarket cross-flow radiator? also not shown is the electric fan mounted in front of the radiator. Ideally this would be behind as it blocks a substantial amount of airflow through the radiator.
