The R/H tickler pin may not be pushing the float down far enough for it to open the float valve?
The tickler roll pins are a push fit in the buttons, so can be adjusted by gripping both parts (with pliers/grips?) taking care to protect the metal surface of the button, and then twist the pin out of the button slightly. Keep adjusting a little at a time, and then re-test until the carb floods as easily as the L/H one.