In a nifty trick I call "hypocrasy", I guess I didn't mention exactly what I did in my WIP, despite my professed preference for show and tell in WIPS.
I mixed up some Mig pigments, if I recall, Europe dust, Russian soil, and dried mud, I was going for a dark brown with a hint of red, and since the subject was Russian, I HAD to put in some Russian soil, even though it is basically black. I put it in a little cup and mixed it, then took a makeup application thingy, foam rather than a Q-tip, and ground it onto the tires, mostly in the tread and depressions. Then I took the M1A1 thumb and simply rubbed the sidewalls and the high spots of the treads, taking off most of the dark pigment, leaving it where it would be after the mud dried and wore off the rest of the tires. The whole process was done "dry", no thinner, water or pigment fixer was used. It worked, but I think it would work a lot better if the detail in the tires was better.
If you look at this WIP, I painted the tires at the top of page 5, by the end of page 6, you can see I have done mud/dirt on the tires. (Yes, it's sitting on the base you walked me through before my first contest.)
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Bill