So the marker light bulb next to the high beam was dead on my 2008 Jetta. I figured out the replacement and the mechanic I know replaced both sides with new bulbs. The light came on when I tested by turning on the dashboard/marker lights without starting the car so I was relieved it was fixed. Then, I started the car and the bulb at the same spot died again. Agh. I went through the fuses and none of them seemed broken. I might have been extremely unlucky with the bulb that it worked for only once or the bulb socket might be faulty. What else could be the issue?
I wouldn't assume the bulb is burnt out, I'd test it in another car or using a 9 volt battery unless you can visually verify it's blown. If it has indeed blown that fast then it could be a manufacturing defect, and I'd try another. If that blows too then you must have too much juice on the circuit, not enough to blow the fuse but enough to burn out a bulb, which is unlikely but can be verified with a multimeter.
If the bulb is okay the problem probably lies with the electrical connection somewhere. One common problem is corrosion on the socket connection itself, you can often see it as a patina. This can be scraped off or cleaned with contact cleaner, I've also used a dremel to polish it off as well.
Other common issues are contacts getting slightly bent, issues in wiring harnesses, pinched wires. These require continuity testing and some patience, but can be worked out by home mechanics.