Google is still indexing 410 pages which was implemented 2-3 month ago. These pages should have gone away at this time.
So, Should it be logical to implement X-Robots-Tag: Noindex,Noarchive while having 410 http status?
What's your suggestion?
No, there is no need for that. As John Mueller said in Webmasters central
From our point of view, in the mid term/long term, a 404 is the same as a 410 for us. So in both of these cases, we drop those URLs from our index.
It is normal if Google stills crawl those URLs from time to time:
We’ll still go back and recheck and make sure those pages are really gone or maybe the pages have come back alive again.
If those pages are still indexed it could be because they don't have much popularity and Googlebot doesn't crawl them very often. Just wait or use the Remove URLs tool to speed up the process.
There is no need to use X-Robots-Tag: Noindex,Noarchive
. Google automatically removes 410 pages from its index within hours of crawling them. (Compared to 404 pages which it will give a 24 grace period to see if they come back.)
Google would usually have crawled and de-indexed a 410 page within 2-3 months.
Look at your log-files - is googlebot visited 410 pages since they become 410? If yes - just wait, if not - make a sitemap containing only 410 pages and upload it into search console.