Guitar makers do this all the time, but they don't use a saw, generally. Create a jig that holds a chisel as a scraper, and then you pull the strips through it, narrowing the space slightly each time.
The idea is to saw oversized and then plane or scrape to thickness. The takeaway here is that 1/8inch strips are best thought of as "binding". And binding has traditionally been made with a scraper.
As for how to get the starter strip, that depends on the kind of wood. Again, guitar makers would probably be doing this with softwood, and the initial cut would just be careful successive cuts with a sharp knife along a scribed line.