I agree and go for the valve as well. The mentioned tap / hit to the carbs is essential 😉
I am doing a lot of work at different twins and the LTD carbs.
Especially after a full cleaning session where everything is checked and adjusted, there is no fuel in the bowl, of course.
After fitting the carbs back again and opening the fuel cock (PRI position) the fuel runs into the bowl and the floater should swim and shut of the fuel. If the bike is on the side stand, the valve may stick in the open position leading to leakage.
I use to keep the bike upright / vertical and then open the fuel cock.
Fuel is running into the bowl and the floater starts to swim. During that time (approx 10 sec) I always tap the carbs with a plastic hammer, a piece of wood or just with my hands a bunch of times. That typically cures that issue.
If there is a leakage after that “ceremony”, dismantle the carbs again and check the stuff around the valve (valve itself, seat, floater, floater setting / fuel level).
Measure the weight of the floaters. They can be untight and filled with fuel which stops them from “swimming”. Dirt at the valve and seat may also cause that leakage.
To test that without to much work you can drain the bowls until empty. Keep the bike upright and have a “hammer” in your hand. Open the fuel cock and often tap the carbs.
Leave the cock open and wait and see if the leakage is gone or still existing.
Hope that helps 😉