Sharpie will also fade with sunlight eventually.
I think what you actually want is to have her sign a piece of paper with a thick round tip felt pen, then have someone with a Foredom tool mounted on a pantograph trace her signature from it so it is engraved into the wood. Some folks have programmable 3D router tables that could do the same thing from a scan of her signature. Scanning also gives you the option to adjust the size and line weight of the signature it to make it whatever size you want before engraving. Another possibility is to have a jeweler pantograph the signature onto some brass plate (rectangular, oval, or whatever tickles your fancy) and then carve a recess into the wood for it and nail or screw it in place. You could also apply epoxy decoupage over top to protect it, though you'd probably want a sealing layer of finish in place first to prevent the epoxy from bleeding into the grain at the recess edges and changing its appearance.
I've also seen engravers put signatures into the gun metal with carbide or diamond bit, then fill them in with gold. The left side of the receiver under the elevation knob might be a candidate location.
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