Thanks for the helpful comments, I will try your suggestions out (I am traveling atm so my inks are not readily available)! A stupid little thing I’ve just tried is to fill the cap with water … and it leaks quite a bit, where the fancy “edge” is situated. So that might be the issue

Do you mean you screw the converter a little to lower the piston and that gets it going again?

Yes, that’s what I am doing. I had no trouble with the cartridge I used before, so I could try that again to identify the converter as the issue. The ink is Parker Quink Black (but two decades old, so possibly alcohol-based? I read something about a change in formula). It is supposed to be one of the more reliable ones.

If I don’t have problem with a cartridge, then I can exclude the cap as the source of the problem, right?

Yup, I’ve google that name and from the looks it could be this one https://www.schmidtpenparts.com/collections/ink-converters/products/schmidt-k1-ink-converter (no labels on the converter)

No springs or balls in the chamber. And I flush the pen regularly, because the damn thing keeps drying up. ;)