I have filters set in place for eBay to apply labels to sold, offers, ended listings, and other important topics. Is there a way to filter all other emails from eBay that do not fall into the above categories and label them other?
You can try to create a filter that looks at the sender and do a negative match against the existing labels.
Has the words: from:email@example.com -label:ebay-sold -label:ebay-ended -label:ebay-offers Apply label: ebay-other
Gmail will probably balk at using
label: in a filter search value, but as long as your "other" filter comes after the others, it will probably work.
Your other option is to take the criteria from your other filters and build a new filter that excludes those criteria.