yes it can go bad, be burned out.
not usually an issue but you can test it by wiring 2 AA batteries in series and touching the leads to the posts on the gauge. it should move to half way.

if your fuel gauge works, you can eliminate the voltage reg from being the issue, but if it doesn't work then that would be my first go to.

the bulb near it going out could be nothing, or ground on that side of the cluster could have an issue. that too might take out the gauge if ground isn't making contact.

any changes done recently?