If the color appears too light, wait until the stain has dried, then apply a second coat. After staining furniture, finishing the wood can help protect it and enhance the appearance of the wood stain.
Penetrating oil finishes are designed to penetrate the wood, not necessarily to sit on top of the floor in a thick wearlayer like a traditional oil-modified or waterborne polyurethane finish.
But the wood is heavily stained. I think the paneling is original to our 1966 house. It doesn’t appear to have a finish ... the main damage will be a black stain — a common problem when ...