Again, thanks for replies Jens, very appreciated.
I have solved the battery issue with both the 1231 and A604. Measuring the voltage at the pins of the battery holder, there was indeed none. So I experimented taking out and replacing the battery a couple of times, cleaning the holder with 99% alcohol and so on. It seems that the battery should be put into the holder VERY lightly (so that it feels very lose and almost falls out). This will ensure contact with the + tab, it seems that's the troublemaker. At this point the RTC works just fine.
A few more questions, if I may.
How did you get the necessary signals from the A600 trapdoor slot for Indivision ECS to work? This is really bewildering to me.
How did you manage to find A1200 and A600 trapdoor slot connectors? I thought they were quite hard to find nowadays.
Any chances of a production rerun of ACA630?