Like most secret societies that wear pointy hoods, the Guglmänner are a bunch of middle-aged men who are bitter about something. In their case, it is the reputation of Bavaria's most famous king, Ludwig II – builder of fairytale castles, patron of Richard Wagner, and the last king of independent Bavaria before it was forced to join the new German Empire in 1871. Ludwig died on 13 June 1886 –128 years ago this Friday – but the Guglmänner are convinced that he did not, as the official version goes, drown in Lake Starnberg after going mad and strangling his physician. In fact, they say, he was shot twice in the back with an early type of air rifle by Otto von Bismarck's secret Prussian agents as he was trying to escape across the lake. So, Bavaria should never have been part of Germany in the first place.

"It's like with Crimea and Ukraine – they never really wanted to belong," senior Guglmann Richard H. says. "The problem was that Ludwig never wanted to be part of the German Empire, but was forced into it because of the war Bavaria lost along with Austria. Ludwig was always working against the empire, and was secretly negotiating with France to get Bavaria free again. In the end the risk was too great for Bismarck – so Ludwig had to go."

Ludwig II with some hooded friends.

The Guglmänner (Gugl is an old word for hood – they are named after the hooded mourners that accompanied medieval funerals) know how to stage a good publicity stunt. They have marched through Munich carrying flaming torches, once sank balloons into Lake Starnberg printed with the slogans "It was murder!" and "The tomb is empty!" and and this year, apart from the usual commemoration, they intend to release a new 15-minute documentary. Based on a historical crime-scene sketch, this will create a "logical causal connection" to explain the "true circumstances" of the king's death.

Despite their special demands (they once lobbied for a Bavarian euro coin featuring Ludwig, rather than Germany's eagle, which is too Prussian for them), the Guglmänner see the EU as an opportunity. "There are other European regions where the people had to become part of nation states in the 18th and 19th centuries," Richard H says. "But today, we could be given independence under the EU. The old nation state is really out of date."

In the Guglmänner's vision, Bavaria is an independent state with its own parliament and government, within the EU. And Richard H wants one other thing: "Of course with a king – because a people need a figure to identify with. It doesn't matter if it's a president or a king. But a king – well, that would suit Bavaria."

• This article was amended on 11 June 2014 because an earlier version quoted Richard H. as saying "The problem was that Ludwig never wanted to be part of the German Empire, but was forced into it because of the war Bavaria lost against Austria." This has been corrected to say "... the war Bavaria lost along with Austria".