Lots of possibilities. However, I think many people are overlooking some things: (Note I am not a shill for Faber-Castel. It is just that their pens seem to be the best overall choice.)
1. Tips with a diameter of 0.3mm or less are pretty much required for basket weave illusion pieces with 1/8" beads. And even then, it is almost impossible to avoid accidently marking adjacent "pixels" with the wrong color. There are very few pens of different colors available with such fine tips. The Faber-Castel pens come in the widest color assortment.
2. True "basket" weave illusion patterns, inspired by Native American baskets, come in a very limited assortment of colors: black, sepia, and sanguine (for Faber-Castel). Faber-Castel and Dick Blick allow you to buy individual pens, as well as collections. It seems that many of the other brands sell only collections. (I have not investigated this rigorously, so don't burn me at the stake.) I don't want to buy a bunch of pens I will never use.
3. Most "artist pens" are intended for use on paper, with a relatively smooth surface. The pen tips in Faber-Castel Artist pens do not last forever, especially if they are used on wood pieces with changing grain patterns and direction. For example, a Basket Weave Illusion platter will have some relatively smooth, side grain areas and some relatively rough, end grain areas. My experience has been that a "brush" tip gets rounded over and blunted much faster than I would like. The F, S, And X tips, which you need for the finest lines, stay "sharp" for only several square inches of beads or so. (I try not to press hard.) Who has experience with the durability of pens from other makers?
I hope I have not offended anyone with these comments. They are given in the true "forum" spirit of healthy discussion. Maybe someone else will produce information about other pen brands which will work better.