Ok That's the fuel crossover The fuel inlet hose attaches to the carb body as you have it. The fuel can freely pass from left to right using this crossover. It does look like yours is broken. There should be a hose barb pointing down.
You can turn just one petcock on and still feed both carbs.
Getting a plastic replace ment, I can'y say where you would find one. You might try pulling out the bad one, taking it to a hardware store and finding a 90 elbox, I'd try to find a brass one, one that has the same size fitting on the carb side.
Then clean the carb body ver well. Use a fuel resistant epoxy to "glue" the brass barb into the carb body.
Do both sides. Now you can attach a hose between these new barb. The stock hose had a wire spring wrapped around it and was5 or 6 inches long.
Hung down from one barb then bent back up to the other.
Leo