I can't remember how it was originally connected in my 2011 x250 Ducato as I replaced it with an aftermarket android unit some time ago.
But if your radio stays on for 20 minutes after the ignition has been turned off, I'd say it has a permanent +12 V, which is managed by the CAN system (which cuts off the power to prevent battery discharge).
With my new aftermarket radio I had to switch two cables (red and yellow, but that was my case!) for the radio to keep the settings. I used a special ISO adapter with additionnal connectors on those two wires that can be easily switched. Now it can be switched on even when the ignition is off. However I have no idea how long it would remain on... But my van is a commercial van in fact.
Check this thread:
Earlier this year we bought a Swift motorhome and quickly ran into the Fiat Ducato 20 minute radio timeout problem. Neither Swift nor Fiat showed any interest in fixing this, but Fiat/Stellantis said that we could replace the radio at our own expense if we weren't happy. Their complete...
www.fiatforum.com
It explains the timeout but doesn't say anything about loosing the settings. I think that someone with a newer model could help. Or try contacting the dealer, perhaps they could confirm what to do.
Have you got an owners' manual for the Daiichi system?