You could always just use a 1:2 step-up transformer from any electrical supply place. Built to work on AC households. They are designed for voltages upto 220 (from 110) and like 5-10 amps, so they should handle your bike output easily.
Shouldn't be too difficult to figure out some way to attach the connections with spade terminals or such.
They cost about $4.99
You will lose a power feed. From memory, there are only 3 power feeds on a Puch; brake lgt/horn, running lamp and headlamp aside from the coil feed. So you'd have to decide which you want to increase to 12v and drop to half amperage. And if you keep running a 20 watt bulb on it as well, it might kill the power (turn-off) your GPS. E.g. not enough current to power both items simultaneously (whichever has the higher resistance will lose out).
Oh, and you'll still need to use a rectified bridge ($2) to convert the circuit to DC.
No batteries to charge and very cheap. But then you've got this ugly box hanging from your bike's frame you'll need to hide somewhere, but still smaller then a gel cell (which you'd also need to hide).
Just a thought.