Think about it for four femtoseconds:
Energy goes into your geyser via the heating element. You can safely ignore other ways energy gets into the water in you geyser, such from the atmosphere (via the geyser housing), various extraterrestrial radiations (eg sunlight or beta/gamma radiation from space) - none of these are significant for our purposes.
Energy leaves your geyser in one of two ways: 1. with the hot water you use, and 2. heat-loss through dissipation, which is a consequence of less-than-perfect geyser insulation.
Let's assume your household uses 3000 litres of hot water per month, at 60 degrees C. Let's further assume that the incoming cold water has an average temperature of 20 degrees C. That means your household needs to raise 3000 litres of water by 40 degrees Celsius in the month.
Now, it takes 4.187 Joules to raise one millilitre of water by one degree Celsius. So 1000 ml takes 4.187 J x 1000 = 4.187 kJ. So, to raise 3000 litres of water by 40 degrees C takes 3000 x 4.187 kJ x 40 = 502 440 kJ. That's it.
Here's the thing: It doesn't matter whether you do that temperature raising over an entire month or over an hour, it takes exactly the same amount of energy.
Since the only possible ways energy leaves your geyser is 1. with the hot water flowing out through the pipe and to your taps, or 2. via dissipation/heat-loss to the atmosphere through the geyser housing (affected by geyser insulation), the only possible way you can make a saving in your hotwater heating bill is by: 1. using less hot water, or 2. heating it less, ie to a lower temperature (turn down the geyser thermostat, but dangerous as mentioned), and 3. insulating the geyser against losses through dissipation.
Those claiming savings by fitting a timer or switching off are in reality using the timer as a psychological aid to reducing their nett monthly consumption of hot water. There is no other possible way in the known universe that your bill can be reduced.
