I am very glad that I found this thread.
My wife and I have 2 tandems. For bikepacking on our mountain tandem, we have frame, handlebar and other bags so a trailer is unnecessary.
For our road tandem; though, I've looked into getting a trailer so that we could go to the store while out on our Sunday morning rides or throw some gear onto it if we want to do a long weekend getaway to a BnB or something. I would prefer a single wheel although some 2 wheel models are very affordable.
Thanks for all of the insights!