Sad face...
My "New" ST - Worzell Gummidge (Number plate ends in WG) appeared to have a dead battery, but in tracing the wires back, it appears that the starter switch is fused and drained the battery to death.
Fortunately, it appears that the ST1100 and the ST1300 have a common switch block, and I have a spare one from my haul of ST1100 spares I bought (along with the panels & stuff).
Now to remove the right side panels so I can find the socket it all clips into.
Gnomad42