I'm highly against this feature request, because having the job pane always on display allows users to see new and interesting job listings while they're at work, without fear of being caught by someone looking over their shoulder.
Let me explain
In a typical week, when I'm viewing Stack Overflow, it's going to be while I'm at my job. I'm not going to spend a lot of my time outside of work on the site (usually). So the best opportunity for me to see job listings is while I'm at work.
The problem with giving users the option of hiding the job pane is that people in your office will now be able to tell that you're looking for another job while using Stack Overflow at work, because if you weren't looking for another job, you wouldn't need to see the job pane, you would be hiding it. Granted, you could fake the excuse that you didn't know that you could hide the job pane, but let's be honest, being put in a position where you have to fake an excuse as to why it looks like you're looking for another job isn't very good.
Having users see job listings while at work is good for Stack Exchange
I also want to point out that it could potentially be better for Stack Exchange if users were able to see new and interesting job listings while at work. What better time to show users new jobs than while they're unhappily slaving away at their current ones?
Being forced to see those job listings while at work is a godsend. It gives people hope that maybe, just maybe, their lives don't have to be so miserable at their current jobs.