When you say "systems developer", I assume you mean the guy who designs/develops/tests the whole system - which is more than just the code written for it. Generally someone who follows a process like this:
or something like it.
And I'm assuming you don't mean "system administrator" which is quite different.
I made that transition - Software Engineer to Systems Engineer - quite by accident. I was looking for a job, a systems job was available, they were willing to hire me...
But I'd say the skill set you need to show to get the job and move ahead is markedly different from software work. Namely:
Systems engineers have to think big. Give up on specializing on a particular language or on coding at all, start learning about how the system you are currently developing software for fits into the bigger world. How do users use it? How is it installed/updated? Where's the business headed? What hardware does it use? What are it's limitations?
Systems engineers have to be a jack of all trades. So learn a broad smattering of technologies in your business domain, with special focus on how pieces integrated. Also, learn how to learn quickly.
Improve your writing and presentation skills - systems engineers are relied upon to explain the big picture to other people, if they can't do that consistently and concisely, they can't be good their jobs. You need to master both written and verbal communication.
Get a grip on all parts of the process - from the moment the customer develops a desire to the point when the customer is done with the system or a part of the system and retires it.
Systems engineers are often seen as the customer's representatives for understanding the problem domain in technical ways that the customer may not be able to grasp. They should be able to help parse this stuff and render it into useful information for software engineers.
For the most part, I expect that anyone who has "systems" in their title has moved pretty far away from any coding language. They may be able to code, but they are by no means hot shots.