Some of the stains might be deep but a sanding and re-finishing is probably in order.

I second the vote for water stains. We had an old window seat that looked very similar -it was water staining for us.

Thank you! I can do the light sanding. Do you think I'd be able to just add more layers of garnet shellac then to try matching the other surfaces or would I have to try staining it first?

Also - a general shellac question - is there a guide for how much coverage to expect from a pound of flakes?

If you just sand and stain, the sanded areas will be lighter when refinished, so sand that entire area so it will take a uniform finish. A coat of benite will help the wood take a finish more evenly. I would use a more durable finish than shellac. My choice would be a polyurethane in perhaps a satin finish. You can get poly with various levels of color or tone, so you should be able to match the other wood fairly closely.

Considering how poorly shellac preforms in the presence of moisture and that shellac can be top coated with most any type finish I secound the motion of moveing away from shellac as new top coat.