I used to do a lot of this in the 70s. Of course, the Ecoflow and similar water based dyes were not yet available, so these techniques apply to spirit dyes.
Old tshirts work fine for wrapping the block, as do other rags, but I would make sure to use 100% cotton. Synthetics or blends may not absorb the dye evenly.
Of course, the background color (eg cordovan or tan)should be applied first, using whatever method you prefer for conventional dying - daubers, sponge, dipping etc. Make sure the base color is thoroughly dry and then wipe the surface briskly with a clean cloth or scrap sheepskin to remove any excess.
Now apply the accent color (eg medium brown) to the rag that’s wrapped around your block. I always tried to get the rag as dry as possible before touching the accent color to the project. Blot the wrapped rag with paper towels as you described, but after that, try rubbing the block lightly but rapidly over some newspaper until the dye trails on the newspaper are barely damp.
Then I block dye the project, using a light touch and rapid back and forth movement. If I wanted certain areas (eg toward the edges) to be darker, I would go over those areas again as needed until the desired affect was achieved. If there is a crease or other solid border, you can block dye that area solid brown (or whatever color you’re using) just by going back and forth over that area repeatedly.
I never used any kind of resist. The stamp impressions always showed up in the background color so long as I used a light touch and avoided oversaturating the rag.
Once everything is thoroughly dry, wipe briskly with a clean rag to remove any excess and apply resoline, tan kote, or other non-oil based finish of your choice.
Hope this helps.