@jharville
ThisItem would be in context of a control that has an Items property. Your buttons appear to be free-standing and not part of a gallery. And, based on your datasource picture, there would be no need anyway.
It looks like you have a single record, single column list for this.
So, your formula would be:
With(First('ServiceGateway Button Tracker'),
Patch('ServiceGateway Button Tracker', {ID: ID, 'Number of Clicks': 'Number of Clicks' + 1})
)
Keep in mind though that due to how PowerApps gets its data, the number of clicks in the app may not reflect the current value in the list and results may not be what you expect.
You could perform a Refresh prior to the above formula, but that may have negative impacts on your app performance. If not a problem, then utilize that.
If it is an issue, you can utilize a PowerAutomate flow instead to perform this outside of the app.
I hope this is helpful for you.