How to make this pattern
Draw a sketch (the two orange lines with a radi) on the front plane.
Then do a sweep cut with a circular profile and select the correct diameter of your circle and select the sketch on the front plane as the path.
Circular pattern of that feature.
How did you make your existing pattern for the bricks? You've basically got half of the work done.
The horizontal lines appear to just go around the part continuously, so those could easily be formed with a revolved cut.
The vertical lines a a little different. For those, I'd create a single line on one level, then pattern that cut with a circular pattern (hopefully like how the flutes were patterned).
You could then repeat the process for each course of bricks.
How to form the cut will somewhat depend on the shape you want it to be. Square, triangular, circular...etc. There are several ways to make it from cut extrude, a cut sweep, a boolean cut from another body.
Can you post your model so we can edit it and see what works?
Sample image and part posted. Model is SW2017.
There are many ways to do this. Maybe someone will post a better method? :)
That looks good. Hopefully some other members will upload their ideas as well, there are plenty of ways to get that pattern.
If you have a chance, check out derived sketches. I think it would work well as a replacement for the sketch2 you've shared.
The current sketch2 relies on selecting many separate contours which can make later edits very difficult.
With derived sketch you'd make all the cuts on one course, derive the sketch to a new reference plane, rotate slightly, make all the cuts on the 2nd course. Then finish up with the linear pattern.
Now you need a great looking rendering of the piece and you'll be on your way to the Popular Model page!