Adrian, this is getting a bit curious.
Tickling lowers the float, raises the level, fuel will then overflow wherever it can, starting at the lowest point of exit, either by the official bleed hole or the bellmouth. In practice it takes a few seconds for fuel to work its way via these exits, but the level rises quickly in the float chamber, spurts out all over your finger, job done. With the tickler plunger released, the needle valve is now jammed shut by float pressure, and there should be no further fuel flow into the carb. Is the tickler sticking down more than it should, when released, and holding the float down?
If your carb is bottom entry, take the top off the float chamber, see if fuel stops flowing. Check the needle can rise fully into the guide hole in the underside of the chamber lid. If fuel still flows past the valve, try raising the needle by hand. Re-assemble with some fuel in the chamber, lower the lid onto the raised needle to make sure it enters the guide hole.
Otherwise a continual drip would indicate a basic assembly error, cracked body, or simply a poorly performing needle valve. Valve seating, needle taper and float height are all suspect. If a metal float, check that is not leaking and there is no fuel sloshing inside to compromise its action. The old test was to dip it in hot water, the air inside expands, watch for bubbles, there's the leak.
Swarfy.
