The cutters used to cut vinyl signs can be used as pen plotters with inexpensive adapters. A busy shop may not want to mess around with one of their cutters, but there are lots of mom-and-pop operations that would doubtless do it for the right price.
There are Youtube videos of people in the vinyl cutting industry using Sharpie markers and cheap rolls of butcher paper to try out designs before committing themselves and slicing up lots of expensive vinyl. Some show the pen adapters for various models of wide-format vinyl cutter in detail.
If the drawing you want is relatively small (less than 12" or 13" wide by any length) someone with a hobby/desktop vinyl cutter could do it. You'll have to ask around or try some of the various web forums dedicated to plotters, though, since 3DHubs (which is what I'd recommend if you were looking for a one-off 3D print or laser cutter job) doesn't have vinyl cutters / cutting plotters as a category.
I just tried looking a decent amount and couldn't find anybody offering contract pen plotter services. Your best bet would probably be to write some code to simulate the way lines look with a pen plotter and render it into an image, then print it with a modern large format printer (which plenty of places offer). They generally have very high print quality and should be able to print enough detail that it'll look like it was drawn with a pen.
Edit: maybe you can use Inkscape to get the pen line effect? I've only used it a bit but it sounds like something it'd be perfect for.
I had a good amount of fun watching it go, though as others have stated, they can take forever to run. The output is gorgeous, and generating real honest-to-goodness engineering drawings on one is a special feeling.
I have a mind to try some blueprinting with it, if I can find a source of drafting film and compatible pens.
Pen plotters have actually had a resurgence lately among hobbyists with the proliferation of affordable CNC controllers and stepper motors, but I don't think many professional shops are operating them regularly. I bet there are some artists using them however, as well as occasional users like you.