Metal polishing
As I stated in my OP, I put a brand new lightbulb in the vacuum, and the headlight works. However, I noticed it was a little dim. On the inside of the lower base cover, I noticed that a metal piece which disperses the light was all rusted.
So today, I decided to try polishing that rusty metal part. After vacuuming the downstairs bathroom earlier, I took the vacuum up to my room and took the cover off. I found that the metal piece was attached with a Phillips screw. I removed the piece and tried washing it with soap and water. That didn't do anything. So I started looking for some polishing products around the house, and found some Goddard's metal polish. I tried it, but it didn't do anything.
But then, I found some Bar Keepers Friend cleanser and polish and tried that. It worked great! It took some elbow grease, but I was able to polish the piece. It didn't make the metal sparkle, but it looks better than it did before. I put the vacuum back together, and the headlight is a little bit brighter.
Here are some before and after pics, along with the products I used. The last pic shows the headlight in action.
