FALCUM,
Being an electrician, from what you have told us, I am guessing that the GFCI (GFI [Ground Fault Circut Interupt]) plug is being shorted by the old timer you were using. The GFI is not a circut breaker like the breakers in you electric panel are, but at the same time they are. A GFI is to prevent you from being shocked by using something that shorts out and causes a ground. I am guessing that at the time the timer is clicking off, it is also causing a ground short, therefore tripping the GFI. If you could trip the main breaker for that circut, remove the GFI and insert a receptical with a 20 amp rating I think that would take care of your problem. Seeing as you have replaced the timer already, Take the old timer and plug it back into the same GFI, set the timer to go off. Do not plug anything into the old timer. Let the timer go off, it should trip the GFI. If it does, plug it into a separate plug and do the same thing to see if it tripps the main braker. I dont think it will, but if it does you know that the Timer is real screwed. If it only trips the GFI, you know its just a little screwed, but in need of servicing/replacing. If it does not trip the GFI, then you are in need of looking into your light setup.
Post back after trying the experiments, and let us know how it goes.