You need to define what you mean by "embedded" when seeking opportunities.
If you are speaking of "new-world embedded", using these large, heavy toolchains to do higher level development for ARM processors and the like (for instance, the IoT craze in silicon valley), I think this could easily be accomplished remotely, and there should still be a lot of opportunify for some time as this IoT group has not yet come to reality and does not appear that they will for some time - So there should be money to be made.
If you are speaking of *real* embedded - Low level, specialized, highly efficient development for a real embedded application, this will be much harder to do remotely as you would need to have a significant lab at home and depending on the scale of the product, would likely need to be in-office in order to be an effective team member.
The latter ("real" embedded developers) are in extremely high demand, very rare, and very well paid, but it would take many years to get enough experience under mentors and with significant enough projects to be taken seriously, so I would recommend you look at the first one. It will not pay as well, and many of the opportunities you find will be short term contract based opportunities, and almost always from a small startup type company that could be gone tomorrow, but it should be an easy path to start building a resume.