Well I'm out at this point; all my experience with a '63 plate 4x4 TA points to low volts (and indeed with other marques - specifically an alternator failure on a VW where each of the equivalent warnings came up as I trudged across Europe - bar the alternator warning which came last!!).
My stop start worked for a while with a brand new battery and replacement volts sensor (found on the negative battery post, which is also disproportionately expensive given its size and function!) but stopped once the routine short commuter drive kicked in and took its toll.
Was the original battery the OEM one (FIAT/ALFA badged)? Was that AGM?? Not sure flooded batteries are used generally for stop/start but I don't have that specific knowledge to say for sure. I do try to find a couple of sources to confirm stuff I read online...