And another one

At a guess, I'd say the finish is shellac, and I believe brushing on a new layer will even out the existing finish, re-dissolving it a bit. Your first picture looks a lot like some of my woodwork, while the second I think I have on a couple window sills.

I need to buy some shellac, but can't decide what shade. If you like the color of your wood, I'd opt for the lightest shade.

Sand down the lumpiness. It is important that you used a sanding block, so just the raised parts are leveled down. You don't want to sand through to wood. Then recoat with shellac.Sandpaper grit should be 400. It's slow but rewarding. Here's an organ lid I did back in june:
B4

Clean it off with a mix of laquer thinner and denatured alcohol (50/50 mix) gently scrubbed with coarse steel wool, and wiped off with soft rags.

It will re-dissolve the crinkled bits and clean off all the old cigarette tars, grease and such.

Then evaluate the color and smoothness. It might or might not need staining and sanding. It will need a coat of something clear and protective, perhaps just more shellac.

Casey- you sure have a way with wood :)

Just as a follow up, only five years later, for anyone who is ever searching for this topic in the future, I did not send first but I did use denatured alcohol and while it did the trick it took a very long time. I should have listened to the expert and sanded the lumps first LOL.

nan-nan ... that's why you need the lacquer thinner plus alcohol. it's a more aggressive solvent.

Thanks for the update, nan-nan. I have an old crazed piano that is going to need something done with the finish at some point, but that is way down on the priority list.

That looks amazing

Walnut (?) dresser before and after the magic of lacquer thinner and alcohol and a LOT of gentle 0000 grade steel wool rubbing. I sloshed it on, waited a couple of minutes, rubbed it gently and wiped off the sludge.

The blackening and "alligatoring" is the result of decades of polish and wax build-up. Beeswax and linseed oil polish recipes will blacken because of something in the wax.

Casey and lazy gardens - you have given me motivation! I have been putting off dealing with my old piano, which looks quite a bit like your before photos. Hopefully my afters will look as good as yours!