As far as I can make out with mine, although it is indeed an automatic two-speed gearbox, it will only change DOWN automatically. To change UP into top gear needs manual assistance, which is what the handle on the right-hand side under the steering wheel is for.
To drive away from standstill, let the revs build up to a noteable degree, then ease off throttle and at same time pull the handle against spring pressure (not too hard or you will pull the handle off the cable as I have done many times!). Revs should noticibly drop. return handle slowly. You should now be in second (top) gear. If revs immideatly rise again, it has not found second. Try again but hold handle out a little longer time. Eventully you will get the feel for it and learn the precise rev range in which it will change. Too little & it will not change, too much & it will not change.
I belive you need to make this manual change every time you want to get top gear!
Note, it will only drop back into first gear when you have slowed to a near standstill. Then you will feel & hear a distinct "clonk". This is it dropping into bottom gear.
As far as I can see, changing gear has no effect on the forward speed. Only on the rev range of the engine.