My mazda 626 was leaking coolant. I replaced the radiator for there is clearly a hole on it. It worked fine for about a month. Then I see some leakage again. And this time it is around the right side of the engine. The only thing I can think of is the water pump because the place is pretty far from the radiator and all the hoses look ok. I did some google and it looks like that replacing the water pump is a pretty big job. All replaced the timing-belt as well. My timing-belt was replaced 2 years ago. Do I have to replace it? Why involve the timing belt?
A defective thermostat which is not fully opening can cause the kind of problem where you have one leak, fix it and then you spring another leak fairly shortly afterwards. So I would first of all check the thermostat. There is also a hose on the right side that goes from the water pump and thermostat to the radiator. My 626 had a bad thermostat and it caused it to leak from the clamps at that hose, which is adjacent to the water pump.
Here is a video which shows you how to check if a thermostat is good or not.
From the position you suggest it does point to the water pump leaking. The timing belt is replaced with the water pump, as is the water pump is replaced with the timing belt as a matter of good practice, because the two parts are together on the front of the engine. This avoids any unnecessary labour costs if the one or other of the components fails, or arrives at replacement time. The book time for a 2 liter 626 timing belt trime is around 2 hours.