Questions would be asked
Scientists are intelligent human beings, not stimulus response machines. As such there would be intelligent discussion about the thing. Questions would be asked, such as:
- How can the stone know that it is being beseeched.
- Is the stone aware of us?
- Is the stone intelligent?
- Is this some sort of strange quantum thing?
- Is the stone alien?
- Is it dangerous? Can it hurt us?
- Can we ask it for gold, money, cure for cancer, etc?
- What are the limits of it's power?
- Should we tell anyone about this?
- Should we use this power?
- Are we gods now?
Not part of any known pattern
Science proceeds by attempting to fit information into known patterns, extending the body of knowledge.
It would be immediately obvious that this was something so far outside the norm that is should be treated with great care. There would not be an obvious way to investigate it because it doesn't form a part of any known pattern.
The scientists would want to come up with ways to approach the problem.
I would anticipate attempts to duplicate the wish granting behaviour. I would also anticipate an attempt to remove a small chip from the stone for analysis.
Successful experiments would be filmed. I would expect these films to be put on youtube and go viral very quickly. I would expect great interest from all corners of the scientific community.
If the rock can indeed grant wishes I would expect great interest from the Pentagon / relevant governing authorities and accompanying security.