OK. Next step in the - starting to be a never ending - story.
I built the clock circuit as per Ben's video instructions (
https://youtu.be/kRlSFm519Bo?si=mSM3vmfU6GLigqLs & following episodes) and it all worked just fine (I swapped the second and third NE555 by an NE556, but it all worked as expected). Put it aside for a while (more like a couple of years). Dug it up a couple of days ago, and hooked it up to a PWR supply, and ... nothing. The PWR supply even went into protection mode and switched off. Couldn't find what went wrong during the time of inactivity, so decided to rebuild the thing re-using the componest on the failing circuit.
The first circuit works fine (blinking LED, speed adjustable with the trimmer).
Added the second circuit, and that's where it gets flaky. The LED lights up and remains lit, when I approach the board to press the button, the LED turns off, with my finger still about an inch away (the LED also doesn't behave the way it should when I do manage to press the button). Seems to be picking up some interference (I used to work in a mainframe environment that got an upgrade from really old mainframes to state-of-the-art stuff like VAX cluster, 100 terminals, etc. One of my colleagues could crash such a terminal by just sitting down in front of it... extremely strange IMO) ? It didn't do that in the first version, that for some misterious reason now has a short somewhere.
Back to the old drawing board I guess. The quest continues.