When you push the tickler it pushes the float down into the bowl, this then lifts the float needle to allow fuel into the bowl. One of those three items is getting stuck or the float is holed and not floating up to close the needle. Take the bowl off, check moving parts are moving ok and test the float isn't leaking. It'll be obvious when you look. Parts are easily available on Mk1 Amals. If you go for new floats then go for the 'stay-up' ones as they are easier to adjust. Replace them and the needles in both carbs at the same time.