Stain is available from most brick yards. It can be applied with a brush, a roller, a garden sprayer or a paint spray gun. I have seen it done several times. The biggest problem I see with it is the sun fades it. It looks really good, then the sun bares down a few years and it gets lighter. This is especially a problem when it's stained to match other brick. There was a crew working on a building near one of my jobs where they had 3 or 4 Wagner sprayers. The all in one airless units with a cord. It was all one guy could do to keep up with cords and keep stain in the cups of the guns. Wagner sprayers are cheap and might be worth the price for a home owner to stain a house.
As far as the mortar, most people just stain over it too. It's just not worth the trouble to mask it off or use a paste or wax to repel the stain. Short nap rollers would be worth trying. I did a chimney like this with paint. I sprayed the mortar with a gray and stipple brushed every single stinking brick. It looked real nice when it was done, but my eyeballs were crossing by the time I was done. I couldn't imagine doing an entire house like that.
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