I completed the test in 2002 and I don't think it has changed since. The GAPAN Assessment seemed to me to primarily test your ability to cope with a Instrument Rating in a high performance aircraft. It tests your coordination, spacial awareness, mental capacity and memory.
The tests will ask you to keep a cross centred on the target with rudder pedals and joystick. The rub is the random movements become more extreme and at some point the controls are reversed on you. Others are following a stream of dots, answering questions on instruments showing different aircraft speeds and attitudes, remembering a string of digits and the final test will require you enter coordinates for grid cells as they are populated and press a special button when a particular symbol is shown. This last task will have you overloaded. Keep your cool and do as much as possible without degrading your accuracy.
I personally don't believe you can prepare much. But I would say that you must undertstand that prioritisation and anticipation are the keys to doing well in these tests. If you develop the habit of thinking ahead and are able to develop a simple effective strategy when you cannot deal with any more information then you should do OK.
The GAPAN test is voluntary and intended for you to learn if you have the right kind of brain for flying training. It probably isn't going to get you job, but it can give you confidence that you are, technically at least, the right stuff.