Where was your self-defined custom trash folder located? Is the account IMAP-connected?

Did you try to create or use a Trash folder under Local Folders? So long as you create it in the account where the server can see it, you are up against whatever configuration the server expects to see. For instance, outlook.com builds all the user folders under Inbox and that's how it works, like it or lump it.

And why do you single out your Trash folder as "a folder that I can reference at a later time" - does this requirement not apply to any other of your folders?

I have two email addresses downloaded to my Thunderbird, one of them automatically provided a sent, junk, drafts, and trash folder. The second email, which I'm inquiring about, automatically provided all but the Trash folder. I tried creating a subfolder under "inbox" and changed the setting to direct deleted emails to that folder, but they are still not being saved there. My account is IMAP connected. Any additional thoughts?

Is most unusual for an email account not to provide a store for deleted messages. While Thunderbird calls it "trash", when using IMAP it may take the name awarded by the server. I have seen variously "bin", "deleted" and "deleted items" used as names for this function.

Have you tried designating the trash folder in Local Folders for this account?

Note that some services, such as gmail's IMAP, have very particular expectations for where you put your deleted items and is best not to change from the defaults. In their system, "deleted" is an alias for "All Mail" .