I've found remote PM jobs are quite rare (I've searched), especially for gigs that might be several time zones away. Provided you even have the requisite experience, and the boss is okay with it, you have to make yourself available for meetings on their time, not yours. That could be a real drag, or not, depending on where you are.

I would target other location independent businesses, or, companies that could use a PM in a specific geographic time zone like SEA. Complete the project(s) before moving on to new gigs in Europe, then rinse and repeat. I have occasionally seen jobs like these on FlexJobs and weworkremotely, but they are out there.

I would market and brand yourself as someone who specializes in a specific market or space like SaaS, etc. So ideally an industry you know well, not just a general PM. Also, build a simple web site with testimonials for social proof and to prove your reliability.

Basically have a plan and strategy that will apply to most everything. Good luck!