There are several ways to create the look of a vintage stencil for your cabinet artwork. I’ve done it a couple of different ways, and you can make your choice based on complexity and resources available.
I typically go for a three-color design (base coat plus two stencils), in keeping with the classic style, which can also be an artistic challenge.
1) Original method. Vintage machines had their paint applied by spraying, stippling or flicking with a brush, usually masked with some type of stencil. This would have been a rigid, thick cardboard paper (or thin wood), with patterns cut into them, and intended for multiple use, possibly hundreds of times.
Advantages: Multiple use (as in production), and has a classic look.
Disadvantages: Investment to make, not as sharp or modern looking.
2) Hand Mask Method. This is as simple as it sounds: use masking tape and paper to create your stencil directly on the cabinet wood. For smaller details, I usually print out a template I’ve designed on the computer. The larger elements I would freehand with some scale drawing for reference. This works best if using mostly straight lines or slight curves. Something more complicated would need a more elaborate method.
Advantage: Cheap.
Disadvantages: One-time use (possibly not repeatable), not as precise.

Creating a stencil by hand, using masking tape and a printed template. Base is white, first color dark blue, third color orange.
3) Pre-cut Stencil. This is usually a one-time use vinyl stencil, and will cost about $150. This is a method to use if you have a very specific pattern in mind, and usually requires a vector artwork drawn on a computer. You might be able to find a local company that can do vinyl cutting, or use a company like Twisted Pins that makes one-time stencils specifically for pinball machines.
Advantages: Very precise complex shapes, exactly rendered.
Disadvantages: Cost, and probably will only get one use.

Using a one-time vinyl stencil to achieve complex shapes and curves. Again, base is white, first pass is dark purple, then pink.
For reference, if you are following the plans for this cabinet and head unit, here are the PNG files for the Side, Front and Head that can be used as a pattern for creating your own artwork:

Stencil for front of cabinet. If you have the vinyl cut professionally, the shop should be able to take your PNG file and convert it into vector artwork, then generate two separate stencils for a three-color design (two plus base).