John Mueller of Google said there is no fixed timeframe or duration for when Google will try to crawl and index a page that was returning a 410 status code. He said on Twitter "there's no fixed duration" for that.
The question was "For how long will googlebot pingback an URL for which 410 status code is issued?" John responded "there's no fixed duration."
A 410 status code is that "therequested resource is no longer available at the server and no forwarding address is known. This condition is expected to be considered permanent. Clients with link editing capabilities SHOULD delete references to the Request-URI after user approval. If the server does not know, or has no facility to determine, whether or not the condition is permanent, the status code 404 (Not Found) SHOULD be used instead. This response is cacheable unless indicated otherwise. The 410 response is primarily intended to assist the task of web maintenance by notifying the recipient that the resource is intentionally unavailable and that the server owners desire that remote links to that resource be removed. Such an event is common for limited-time, promotional services and for resources belonging to individuals no longer working at the server's site. It is not necessary to mark all permanently unavailable resources as "gone" or to keep the mark for any length of time -- that is left to the discretion of the server owner."
There's no fixed duration.
— 🍌 John 🍌 (@JohnMu) March 16, 2020
Forum discussion at Twitter.