Considering they were installed 30 years ago, my fake bricks have held up well, but were starting to have a brownish tinge on the top edges that wouldn't dust off with a clean paintbrush or cleaner on a rag.

I decided to try painting the top edges to encapsulate the dirt and cover it up. This involved a lot of bricks, but it only took a couple of hours and worked pretty well.
The paint I found was a latex enamel with 'best if used by 6/30/1983' written on the can lid, but it stirred up okay. It had been thinned down a lot, or thinned itself over time, so it was more of a whitewash than paint, but soaked into the bricks nicely and blended with their native color.
Someday I might get a better paint and just paint them on all exposed surfaces so they really will be a better surface to wipe down.
When I got done, I sat on the porch and ate some popcorn. It really is a beautiful day today, probably the warmest so far this year, about 78 degrees.