Sun visor and vanity light

[NickC]

My 2004 Jetta's driver side vanity light (the one above the sun visor) is not working. Normally, when the mirror door is opened, it should light up but it's not.

At first I thought it was the bulb, but replacing that didn't help. Then, tinkering some more, I realized it must be a loose wire because when I rotate the visor about 45 degrees (as if to block sun from the side), the light comes on.

I was trying to remove the visor to see if I could find something simple. I removed the screw holding the visor in place, but it didn't come out. Seemed to be attached pretty firmly. How can the visor be removed? I didn't just want to tug on it. Hopefully there is a simple retaining clip, etc., that can allow it to be removed.

And more importantly, is the light issue an easy thing to fix?