Are these searches for goods or services that might be obtained locally?
Google's results... even on desktop... are hyper-localized. Conceivably, mobile serps might be more finely tuned with regard to location than desktop results, and this could make a difference. Several years ago, I saw results for a branded on-sale item change on a desktop in relation to distance from a store that had them in stock. These were roughly two or three mile increments. Results on mobile now are probably much more sensitive to location than those results were.
Also, Google gives different geo weightings to different kinds of businesses and location factors, and personalization is a factor.
Regard tools, again, please note. that we generally do not discuss SEO tools in this forum. Two weeks ago, you posted a question about rank checking tools, and we made an exception for your question. Several members explained why rank-checking was difficult because of personalization (which includes location).
Further discussion about tools should take place on that thread, which I'm noting below... You can add further questions about what you're looking for on that thread. Any tool discussion on this thread, though, will be removed without notice.
I don't think that you will find the kind of tool you're looking for, and it's not likely that it exists. Suggest Accurate Rank Tracking Tools https://www.webmasterworld.com/google/4957359.htm