Closing the loop on this issue in case its helpful to anyone in the future.
I checked the ArcGIS Server logs when the Gauge element produced "Cannot Access Data" and it recorded the following error:
- Geodatabase error: Insufficient permissions[42000:[Microsoft][ODBC Driver 17 for SQL Server][SQL Server]The SELECT permission was denied on the object 'XXX_evw', database 'XXX', schema 'XXX'.]. Insufficient permissions.
Turns out the arcgis server user had permissions to the feature class in the enterprise geodatabase, but not the versioned view. In ArcCatalog, I regranted SELECT privileges on the feature class to the arcgis server user and now I can used the Gauge element with the layer.