In most applications, they block both hoses (like the heater valve does). But, I'm more concerned about your overheating problem.
Your '61 LeSabre is a great car. My uncle had a wagon, new. We took a big family trip over the Rockies, and the Buick had to stop periodically because of heat issues. (Our car didn't). That was in '61. Certainly, those Buicks ran just fine with 'regular' driving, but I'm not surprised you are having problems today.
I don't have answers for you regarding system capacity, etc. Lack of flow is always the cause of overheating.
Believe it or not, a big air pocket will cause overheating as well. It's still lack of flow. At the factory, they vacuum the system, then fill, for two reasons. If the vac leaks, there's no sense in filling, and, once all the air is out fluid fills all the voids.
If you rad is restricted, a radiator shop can do a flow check. Thermostat sticking closed is another cause. If the pump and hoses are flowing properly, you may want to do a high pressure block flush to clear out piles of rust that settled around the cylinders, etc. Beyond that means pulling the heads and/or block to get inside freeze plugs and clean all the passages using a wire to dislodge rust. Freeze plugs would then be replaced, and new head gasket holes are already clear.
A MAJOR recent problem, is when old type anti-freeze is mixed with the new 100,000 mile coolant. They are NOT compatible, and when mixed, turn to mud that is real hard to pump.
Collectively speaking, spending more money on products doesn't mean you're doing your car a favor. Mixing incompatible fluids in the rad, brakes, and crankcase is common with too many home mechanics.
I hope this helps. It would be a treat to see your Buick on the road again.
_________________________
"We've got to pause and ask ourselves: How much clean air do we need?"
--Lee Iacocca