Don't dab, saturate and scrub. If you get to raw wood with denatured alcohol, it's shellac.

Does it look like it might be shellac?

That's graining; a strie (stree-ay) done with the fine-toothed graining comb. The clear coat could be oil varnish or shellac. If the base color was painted directly on bare wood, you are never going to have an antique-looking railing, not in our lifetimes; you will have to sand pretty deep to get the paint out.
IfOTOH, the graining is newer, and applied on a previous finish, you may have a better result getting back to the old lumber's desirable quality.
Casey

Casey,
Thanks so much! I think it may be the original finish: if I look at a place where the wood is chipped, there does not appear to be another layer underneath.
Does that mean my best option is to paint over the whole lot?