For many years I put black fabric paint through an airpen, a small gizmo with a syringe and surgical needle on it, with a tiny air pump, and wrote with that. It's NOT an airbrush, and it made the most marvelous rich, crispy black lines. I've switched lately to using my airbrush for a little bigger lines, and some acrylic paint markers by Posca, for a more controllable line.
The trade off is that markers cost a lot more to use, and then you throw them out. Airbrush is reusable but has a LOT Of cleaning involved, besides the learning curve and cost of buying it in the first place. The airpen is not cheap either and very hard to learn to use and clean. I no longer teach any of that stuff. I only teach freehand drawing on paper now.
So my advice is to look at the Posca paint markers on Amazon or elsewhere. The fine line ones are what you can get a somewhat small line with, but nothing like the lines you mentioned, with ultra-fine Sharpies. Which fade and look terrible on cloth! They are not meant for cloth anyhow.
I used to write with Rub-a-Dub Sharpie markers, but would embroider over those lines. Rub-a-Dub is the only Sharpie pen meant for use on cloth, except for those Stains things, which are transparent and pitiful!
Rub-a-Dubs are great on paper, but they quit making them, so you pay a lot for them now.
Oh, I forgot to say that the Posca Markers are opaque, and that makes them more substantial looking on fabric. AND I always, always headset my paints, markers, etc, with a hot, dry iron, working slowly and ironing on the back, wearing my respirator and using a big exhaust fan in the window across the ironing board from me. Everything gets heat set at each stage of making my work. So there you are!