Do I have to pay you if you cannot find the requested information?
Yes. You must pay for the time I have spent researching and writing, even if I cannot find the requested information. Various circumstances can lead to inconclusive research, for instance if the authorized time is insufficient. Other times, I may have had plenty of time for research but had to conclude that the information is not available in any known sources.
I have only once as a professional genealogist had to report zero findings to a client. The reason for the lack of findings was that the client could provide very few known details about the person of interest. I had made the high risk of non-discovery clear to the client beforehand.
The research time is never wasted, because the research report will show what I researched for in each source, what my findings were, and how the findings relate to your research question.