When should I use a Gone (410) redirect instead of Permanent (301)?

In Settings → SEO Settings → Redirects, the Type decides what visitors and Google are told:

• Permanent (301): the page has moved for good. Visitors are sent to the New path and its ranking passes on. Use this when there's a replacement.
• Temporary (302): the page will come back. The ranking stays with the old address.
• Gone (410): the page is deleted for good and there's nowhere to send people. Google drops it faster than with a normal "not found".

For a 410, enter the Old path, choose Gone (410) (no New path needed) and click Add redirect. Redirects are part of the Advanced SEO plugin.