I ask because I thought opening up this post that I was going to start with an easy answer, but the more I thought about it, the less I was sure what "work ethic" even meant.
So, I looked it up:
"The principle that hard work is intrinsically virtuous or worthy of reward."
So, I came to this post/question absolutely certain that "a strong work ethic" was absolutely something I agreed with and would look for in myself and colleagues. Now, I am not so sure.
Is "hard work intrinsically virtuous"? Is working harder rather than smarter more worthy of reward? There are plenty of jobs where real unpleasant, hard work is required yet is often of little value. The architect will get more reward than the foreman who will in turn get more reward than the person spaying gunite. Life seems full of counter examples to "hard work is intrinsically virtuous".
Even when comparing people in the same job...
Would I rather work with a partner who was "lazy" and produced 10 widgets because they knew how to best use their tools, or would I rather work with someone industrious who produced 10 widgets through sheer force of will? I think the first one rather than the second.
Ultimately (to try to actually answer your question). If I did not know a candidate or their actual "work ethic", I would ask them to tell me about a time/job/project/assignment that was a (potential) failure and what they did during and after the project as it was ending. What did they personally do to mitigate the failure and after the project had ended what did they personally take away from the post mortem.
Have you had a problem with hiring people who slack off and get nothing done? Are you asking how you find people who will work 80 hour weeks for months on end without overtime and without quitting on you?
To give an example, thinking back to school days when doing a group project. There's the person that ends up doing all the work vs the person that takes advantage and just rides along until they are bugged enough to do something.
Just because someone feels compelled to do good work does not mean they actually take steps to do good work.
1) They might neither know how to nor know how to ask.
2) They might have a problem which is really hard for them to solve but really obvious for everyone else they know -- consequently they don't have anyone they can ask.
3) They might be deliriously sleep-deprived.
4) They might have no idea how priorities work.
5) They might be confused but too embarrassed to ask questions.
6) They might have fallen behind on their piece due to some normal reasons and then fallen into a spiral of anxiety.
7) They might be mis-judging how good their work is.
