Hey,
Today I was working on the Punto to get it ready for APK (dutch MOT) and the reverse lights didn't work, changed the bulbs, also nothing...
So i switched the reverse switch with the one from my 1998 cinquecento 1.1 but that didn't work either,
Any of you guys who know what it could be??

It's a simple enough circuit. There's a switch on the gearbox (front, near the selector box) which may have become disconnected (2 pin connector). I'd test there, first. Once that's proven to work, test for 12v (positive and negative) at the light itself.

I already checked the switch, and also checked if the system works with a new fuse, bulbs and another switch, and it doesn't
So I have to check for 12V on the connectors this week,
I'll update you later because i dont have the car here at home

my guess would be corroded bulb connectors if its not the switch, bulb or fuse.