For Faux Calligraphy we use markers instead of brush pens or a calligraphy quill. You can use any marker, it just needs to have a tip that can do narrow lines as well as broad lines.
If you've followed my Instagram feed you've seen me use several different brand markers in the past. But now I pretty much only use these, the Faber-Castell 24 duo-tips. I like these so much, the colors are fun (48 different colors to choose from), and they're a really affordable alternative to expensive brush pens.
Don't confuse these for brush pens or paint pens, they're markers. But markers are the tool I choose for my faux calligraphy projects.