Update: I replaced the electronic ignition module (black box) with a spare Gamma one I had. It looked new and was in original Fiat/Lancia box. The car run idling for about 40 minutes and just as I thought "it's fixed!" it cut off

So it's not the ignition module and it's definitely an ignition problem as I managed to test for a spark again when it wasn't running. I also measured the resistance/impedance across the wires from the distributor and there's nothing while I would expect something if there's a coil at the other end of the wires. The plan was to check again once the car started but when I tried about an hour and a half later it still refused to start. I'll try again tomorrow...
Geoff, an old Gamma distributor would be nice

I'm sure I can transfer the pickup from it to the Beta distributor.
Unipart closed down last year! Their Lincoln road shop is now a Eurospares shop and they are quite useless as they ask for the registration number and then just give you what their computer says. I bought a Gamma battery from them and they supplied the wrong one but insisted that it was the correct battery for my car because "the computer said it was"

I miss Unipart....
Neil, thanks for the offer but I hope to have the Trevi fixed and in use before the next meeting which I thought is on Sunday 17th May and not 11th. I know because it's the day before I go to Vienna for the Eurovision Song Contest!

There's no vacuum advance on my Trevi's distributor. Where and how did you manage to get a brand new pickup?