It seem (but I can't be sure) they went straight in with a clear amber lacquer, then a reddy-brown one, then blacc for a standard tobacco sunburst. Where it's flaked it's left the wood clean as a whistle. There are a couple of spots (the first to go) where I glued the chips (big ones) back on, hopefully I just used white PVA.
Happy with it as it is for the moment, but the rate seems to have sped up (the bit by the lower horn only 'burst open' this month) perhaps by me keeping it indoors. Here's a recent pic, but even more unseen chipping around the edges).
An alternative would be to stabilise it (white PVA under where it's lifting?) then sand the edges smooth. That would be more or less reversible.
The going rate for one in good condition is about £300 and TBH I'm more interested in playing it than using it as an investment.