On a standard frost-free fridge's

Question

On a standard frost-free fridge's lower section (main door) there is a funnel shaped type of cup on it's upper-back ceiling section that evacuates the overflow of water when the ''defrost timer'' goes on. the one I have to fix keeps overflowing inside the fridge not to say that it keeps freezing anything in that area (say a glass of water as a test). I've cleaned the outgoing drain hose as well as it's ''S'' plastic shaped section installed outside on the upper back of the fridg but, no succes achieved. Should I assume a defective defrost timer...Your help would be much appreciated. Thanks Gilles.