I am slow to pick up on this one too, but let me add to it. My early S1 panel is wood veneer on a fairly brittle looking plastic moulding. It’s quite light in colour and I have always thought it to be straight-grain walnut with as eyore says, a satin finish. Later S2 cars have an even lighter veneer on plywood and you can see the laminations around the instrument holes.
Peter Pompilii had his S2 Sport done with rose-wood and it is possible that Mark Webb might know where he went to for this.
And, for what it's worth - the Flavia 1800 Pininifarina Coupe had a wooden instrument panel, whereas the other 1800 Flavias didn't.