If the domain name is not with any auction house partner (I think that’s what you’re saying), then you can use a drop catch service anytime: https://www.domainsherpa.com/domain-name-backorder-services/ They do not make your order public information as NameJet and others do by sharing how many bids are placed on a domain name and thereby driving interest.
If you buy keyword specific domains, you're really buying the type in traffic.  I use the URL builder and redirect through that URL so you can see how much traffic your getting from the keyword domain.  There seems to be no rythme or reason to what keyword domains deliver traffic and what don't.  By tracking traffic with the Google URL builder you get a feel for what names are giving you traffic and which are not. ie. the plural, the singular, two words, three words, the possessive, etc.
See https://www.domainsherpa.com/domain-name-dictionary/life-cycle-of-a-typical-gtld-domain-name/. They start it in auction listings after it expires and before pending delete. I don’t know the exact dates, but if you monitor it you’ll see it go from auction, to closeout, to drop. You’ll need an auctions.godaddy.com account (I believe $5 per year) to bid and buy.
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We do not only have Expired Domains, but you can also find lists of Deleted Domains for a lot of TLDs. Deleted Domains or Dropped Domains are available for registration and can be picked up for just the normal regfee at your preferred domain registrar! All Domains have the typical SEO relevant data, like Number of Backlinks, Archive.org Birth Date and a lot more.