100% not Kauri .. the grain is different. (I also would place a high bet on it not being Mahogany, but beyond that!?!)
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How about NZ Rimu? Hard wood with similar grain and colours.
I think the colour is closer to red cedar.
Rimu tends to have more contrast in the timber, and you don't get the 'flame' kind of patterns in the grain.
Taraire matches the grain, but is more blond than what you have there, except for the picture on the right.
That would be a perfect match with my computer desktop (Taraire).
Found it was repaired on one corner (or maybe started that way). Due to an accident Tung oil was used. Will research to see if shellac will go over Tung oil.
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Didn't like the dark patches so waited and finally sanded then applied water based satin lacquer.
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Could it be Myrtle?