Hi Michael. Before anything else, I’ll just point out the Paintstop plugin, located in the Document menu, which would allow you to paint with a lot of the features and characteristics of a dedicated paint app. That would be more useful for texture work rather than sculpting, but still an interesting plug-in to be aware of.
As to how to do this in ZBrush proper for the purposes of sculpting, it mostly comes down to stroke and alpha selection for a given brush. Combining the “Freehand” or “Dots” stroke type (“Freehand” and “Dots” are interchangeable in most situations) with a speckled alpha type to mimic brush bristles is how you would do this in most cases. See the “Rake” brush for an example.
Bear in mind the mesh needs enough resolution to be able to pick up the “bristle” detail, and you may need to tweak the stroke settings–reducing Z intensity to a low value will produce more natural looking results. Using a brush like the Layer brush instead of the Standard brush can produce a flatter stroke that behaves more like actual paint, depending on what you want to do.
A slow, firm stroke will produce the best results. Lazy Mouse is enabled by default on many brushes, and disabling it may let you paint more freely with more responsiveness, producing more natural effects in this situation. Lazy Mouse is toggled with “L” by default.
There are also certain options in the Brush palette that may aid you in creating advanced brush effects that lend themselves to this. See the Brush > Modifiers > Trails feature, and the Brush > Alpha and Texture > Tiling features.