Deleted emails do not go to my On My Mac > Trash mailbox, rather they just disappear.

Is there another Trash mailbox that I"m missing?

There are two accounts in my Mail app, one for me and one for my wife. Each of us has our own Trash. The icon looks like a trash can, in contrast to the On My Mac icon, which is generic. Our deleted emails go into our individual Trash, and nothing goes into the On My Mac trash. I have no idea why this happens but it seems to parallel your observation to some degree.

Hover the mouse over your account mailbox. When you do this, do you see the > symbol? If so, click it to reveal extra mailboxes.

Thanks for pointing me in the right direction, Jon.

Hovering over "Favorites" revealed a plus sign which enabled me to restore the trash mailbox I was missing.

(I've deleted the "On My Mac" trash mailbox.)