What I'm basically after, is a RPi replacement of this 12v timer
You can do this with a simple npn transistor circuit. The process is roughly as follows
1. Work out the maximum current needed (add a little 10-20% for good measure), assuming this is less than a few hundred mA, a transistor will do the job.
2. From the datasheet for the transistor find out the current gain of the transistor (called hfe) - at the maximum current . This tells how many mA you need to supply at the base to get the current you need.
3. Now stop and check that this base current does not exceed the maximum that the GPIO can provide. This is the most important step. Assuming does not, continue...
4. From the datasheet find out the base/emitter voltage drop (usually 0.6-0.7v)
5. using Ohms law, the fact that you are using a 3.3v signal and the V in step 4, calculate the size of the base resistor. e.g. Rb=(3.3-0.7/required base current)
6. Now if you were to build this and turn the GPIO on the required current will flow from the collector.
The point here is that whilst it is important to protect the GPIO with a suitable base resistor, you also need to make sure that the base resistor is not so large that it does not provide enough current for the application being switched. It is a common mistake to do the former without considering the latter.