Look at the Polychromatic Segmented Pen tutorial in the library. Should be able to modify that into a nice brick pattern. There are two ways I make four brick patterns, one with equal size bricks and one with different size bricks. One uses four laminated wood segments for equal size bricks. I use three layered segments to make a Flemish Bond design that looks great. You get two long bricks and two short bricks. Do a quick search to see a Flemish Bond Wall .
For a brick pen with a four bricks pen per segment layer with two long and two narrow bricks try this. I use three 1-1/8" wide segments of any lengthen you want to work with. Glue segments on top and bottom with spacers, ( dyed veneer), between the top, center and bottom segments. It looks like a sandwich from end view with veneer in between the three layers. When turned, I get what looks like four bricks with the veneer as grout. If I make the thickness of the center segment a third or fourth of the final pen barrel size you get a pattern of two long bricks and two narrow end on bricks. Works well for barrels with little taper but not for one with a lot of taper.
Segment thickness is dictated by pen barrel diameter. If you are shooting for a pen barrel with a diameter of .75" I use a .20-25" thick center strip segment glued to two .45" outer segments. You have to allow for and adjust for the veneer thickness. Looking for a final blank that is square. If you get a 1 1/8" X 1 1/4" blank just run if through the thickness sander/planer/table saw to get it square. Be sure to take a little off both sides. Made that mistake once and ended up with a blank that had to be re-trimmed to get square and pattern centered.
Dyed black or grey veneer works for the joints and is cheap. Put one piece of veneer in between each long segment when gluing them up. Then drill the blank. Cut the segments to thickness of your bricks. Cut the veneer into squares. Drill the veneer spacers for the horizontal grout lines. Stack them like sheets of paper and drill them on the drill press. I then put the blanks on a long, (10") brass tube of the proper diameter. Alternate brick, veneer and brick segments. Turn the segments by hand to proper alignment and tack with thin CA. I put pressure on the segments to make the grout lines as thin as possible. I cheat by using a piece of UMHVW plastic with a hole in it to hold the assembly. Then clamp to force everything together. Thin CA to tack, remove the brass tube and flood the inside hole. Might need to re-drill the hole when the CA cures. If you want to make a lot of them just keep stacking them into as many blanks as you want. If you are sloppy you will glue your blanks to your tube but that is no a big problem. Just cut it to size and turn it into a pen. Flood often with thin CA to make sure the segment don't blow up.
Now if you are set to use acrylic then you need to watch the thickness of pick guard. At .060 or .090 your grout will be rather thick. I would look for something thinner if possible. .040-.050" maybe. It is all about the proportions of grout seams to brick size. Get it too thin and it might disappear or worse get it too thick and have the grout over power the brick pattern. You might think about ripping your own acrylic spaces from a block of black acrylic. Should be easy to have someone here cast a large block of black acrylic for you. Then rip or on your table saw or cut it into thin strips on a band saw. But you are looking at two thirds waste. Might be able to find a thin acrylic sheet from a vender off the internet. Anything under a 1/16" should work.
You might look at yellow dyed, stabilized woods for your bricks. Then they would work with the dyed veneer for grout. Build a prototype of a couple different designs and see what works best.
