I've tried swapping the cables, and it worked from the first try.
I now have picture on the 7" screen, which is now connected to hdmi1 and when I connect the 27" monitor to hdmi0, I get picture on the monitor. The 7" screen then displays a rainbow color screen and then goes blank.
The 7" screen only displays the launching screen, when I play a game.
I immediately tried an arcade game, the launching screen displayed, but then went back to the main menu.
I've tried other consoles, they all seem to work.
I've tried 2 other arcade games, which seems to work.
Coincidence or not, the game I tried first has a bezel overlay.
Maybe the monitor can't handle that for some reason ?
I will disable the bezel and see if it runs then.