Furniture, Wood and Cabinetry Finishing - stripping process ?

i have 2 60 year old cabinet doors that each frame a veneered piece of plywood. i've heated gunned the first two layers of paint off. i'm now down to a dark stain and probably varnish level. i've been using a low odor chemical stipper to take the varnish and initial layer of stain off. wood doesn't seem to be getting much lighter. here's my question:

am i supposed to begin using steel wool to rub down to the wood (with a wet layer of stripper) to get it lighter or am i looking at many removal layers of chemical stripper with a plastic putty knife?

if i should be rubbing it down, am i supposed to wiping the removal excess with paper towels?

thanks.

Ordinarily, you wait until the stripper causes the finish to lift off, then scrape the majority off. The steel wool step would follow to remove the stain and remaining finish.