The only proof is when you visit and see them probably make rain in a place where meteorological report has forecasted there will be no rain. Or withhold rain for days in the middle of rainy season. Road Construction Companies hire them for the job. It might sound rocket science to you but it is very simple only that they wouldn't reveal the secrete to anyone outside their circles. I guess you would be shocked to see it happen but that's not all they can do.
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Show a hundred years of rainfall data, or more. This is part of what modern science DOES.

Then show a record of dates, times, and places proving cause and effect.

Then show that this "man induced shaman rainfall" is statistically signifcant WHEN COMPARED to a control group, which might be a similar region some distance away.

You see? The scientific process is not the enemy of your shaman. It can prove your assertion, or it can refute it. But your assertion is not proved by your words alone.