FWIW: from a non-mechanic TR6 owner.
1. It's easy to drop both float bowls (6 screws each)
w/out removing the carbs from the manifold.
2. Take off both fuel lines into the carbs.
3. the floats will rotate downward and the fuel metering
valves will drop open by gravity. Gently lift the floats
to make sure they are filled with AIR not fuel.
4. Spray carb cleaner into both carb fuel inlet pipes.
If crud is there or the metering valve is stuck, the carb
cleaner should fix the problem. Do this procedure a few times.
5. Lift each carb piston and spray carb cleaner downward into
the needle holes. If crud or "a small bit of meat" is present,
the cleaner should blow it clean. Do this a few times.
6. Rub some engine oil on the float bowl gaskets (replace them
if you have two) and reinstall the float bowls.
If this corrects the leak- OK! If not - you've ruled out several
possible leak causes and cleaned your carbs a bit.
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Bearing in mind, Tinster isn't really a knowledgeable TR6
mechanic but he DID stay at a Holliday Inn in Manaus, Brazil
best of luck and keep us posted.
tinster
1969 Carbs as seen from below w/ bowls removed: