I know that this topic is discussed in the community many times, but the difference is that I am not using any custom success event with eVar. But I am producing a report with just Unique Visitor as a metric.
I set this eVar on every page, but I still get “None” row in the report against Unique Visitor. (about < 5%)
Also, if I add instances in the metric along with Unique Visitor, I get "0" for instances against "None". This proves that I am setting this eVar every time.
Instances not having "None" doesn't prove that you are setting it on every page. Instances only shows the count of how many times it was set. In short, Instances will never have "None".
If you want to check the pages where the evar was not set, you can do so through the Data Warehouse reports. You will need to get the evar report broken down by page URL. You can also use segment to achieve this.
if you would like to find the exact content of the hits where the evar value was not set or persisting, you can do this through the Data Feeds under Admin.