The short answer is that there is no API that will return the information that are trying to get. You can look at this post: https://community.atlassian.com/t5/Jira-Core-questions/How-to-obtain-ItemId-in-api-2-dashboard-dashboardId-items-itemId/qaq-p/189400. As you will see, there is no API that will return to you the itemid for the dashboard gadget. Without that, you can't access the properties. Further, if the gadget doesn't have a property that tracks access, there is no other way to get that information.
The only alternative that I can think of is to scrape the access logs looking for access to specific dashboards. If you know what gadgets appear on the dashboard and when they were added or removed, you would have a reasonable estimate of the number of times a gadget was used.
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