Hi Tom,
The preferred approach by eBird is to simply create a checklist for the outing where you searched for the rarity, and have that be a complete checklist of all the species you were able to identify. You can put a checklist comment in explaining that you were unable to find the target bird, and of course not include it among the birds you did find in the list. That would be sufficient.
eBird has repeatedly indicated that they do NOT want folks entering "0" for an unfound species.
"
Counts of zero birds - not including a bird in your checklist implies a count of zero on a
complete checklist, so please don't enter '0' as a number. The one rare exception to this is when using the
UN Breeding Code."
Eric
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Eric DeFonso
Boulder County, CO