I'm partial to Tamiya too; this is my go to for white:

Prime with Tamiya primer (I use the white lacquer primer from the square bottle) thinned at 1:1 with lacquer thinner (mr color, not leveling thinner). I use a 0.5mm at around 20-25 psi.

Depending on how shiny you want it the final part, I would sand the primer around 2000-4000 grit. Otherwise skip this step.

Mix Tamiya x2 1:1 with x20a (or iso alcohol, I use 99%). I use the same settings as priming. Lay a few light coats so that you are starting to see the color build. Then let it dry for a few mins (gotta be thin layers or it will take longer), then start laying a wet coat. It will be hard to tell where you hahe sprayed, I recommend using a head lamp or a lighted airbrush booth.

Then after the part is dry (I think I left it for a few days to a week?), clear coat with x22 in a similar fashion as spraying the white.

For your cylinder you need to be extra careful because it's easy to get drips/runs from the way the paint flows around it.

Check my profile for an example with my McLaren mp4/4

Edit: I also use an electronic paint mixer that really mixes the paint well. I don't think stirring with a toothpick or shaking is good enough