Sounds like the lines have an air block(s) at the lowest point before the engines or an air leak in the lines. The petcock on the teardrop may be plugged. Solving the air leak problem is obvious.
For the air block, first make sure the teardrop cap is vented. A siphon won't flow unless it gets air above the level of fuel. Make sure the petcock is turned on. Test by disconnecting at the T and checking flow. Reconnect the line.
Remove the air block by removing the gas caps on the engines and slightly pressurizing the teardrop tank with it at least half full. This should force fuel through the lines to the engines, clearing the air block(s).
Be aware that the siphon probably won't stop when the engines' tanks are full. You will have to manually turn the petcock on/off.
After thinking about your setup for a while I have another idea. If you plug the vents on your engines' tanks' caps and seal the input lines at the top of the tanks coming from the teardrop, the engines should draw (from the very slight negative pressure from those itty bitty fuel pump diaphragms) directly from the teardrop to the engine tanks. When the engines aren't running, they won't draw. However any air leak in the lines would prevent this and also cause a fuel leak after they are shut down, even though you turn off the petcock.
This is interesting. Please keep us advised of the outcome.
Good luck.
Ted
PS - If you do set it up for drawing directly be advised that you will not be able to remove the engines' tanks' caps with fuel in all the lines. The tanks will overflow slightly. That may be of no concern to you, but I hate fuel spills however slight. Valves at the top of the tanks would allow you to do so.
You could also connect the teardrop lines directly to the carbs once the no siphon problem is solved.