Modern Vespa

The 6V vintage Vespas have 3 coils on their stators: the ignition coil, a 6V coil (green wire) feeding the horn and a 12V coil with a blue wire feeding the brake light, and a yellow wire feeding the lights.

At present the brake light burns weakly, and the light bulbs get blown because they get 30V+.

It is the first time ever that I have encountered this problem. Is the 12V coil faulty, or what could be the problem?

The bulbs (obviously) will blow if they see 30v. I'm not to aware of your setup but you must have a regulator fitted between coils and your bulbs to keep the ac voltage stable right?
Kevin

It's a stupidly designed balanced system. You need to have all the bulbs at the correct required wattage, a healthy loom and all contacts / connections clean and tight...

My setup is as per the wiring diagram. New loom and bulbs, so I will have to check all the connections

-1% on stupidly
When these bees were designed there were no common streetlights, like we have today. Any light at all was glaringly obvious. But first you could hear it coming anyway. In the old maintenance manuals the recommended electrical disposable was Vaseline on the contacts. The properties of Vaseline kept the vibration down and the metals from corroding, both of which make the system less durable. If durability is what you desire only following the old rules work. Nobody wants to ride a Christmas tree light set, used only once a year. Never forget everything was designed with pencils.
How many times I've saved someone in their travels just by adding petroleum to the contacts is lost to me. I guess it's my universal tax I pay to not having the struggle of such trifles. Aloha

This. Every single bulb needs to be the stated wattage in the manual/wiring diagram. That would be the first thing to check.