If you're looking for ongoing part-time contracting, I have successfully landed multiple contracting jobs by applying to places that were looking for full time work, for whom my skills were an exceptionally good fit, and saying "I know you weren't thinking of part-time remote contractors, but I'm a really good fit, would you consider it?"
Lots of places have just never seriously considered it, but faced with a hot prospect, will do so. And lots of places out there are actually wrestling with the issue of needing extra work, but not having enough to justify the obligation of hiring permanent full time.