You have lots of choices in the 13' class, and Trail Mite is the same basic layout as
Scamp,
Boler, and many others. Trillium is very similar, but a bit more upscale.
Scamp is pretty much the only basic 13'er still in production, though there are some current upscale competitors like
Armadillo and
Happier Camper.
Any of them will be a good choice for your Odyssey. Consider adding a transmission cooler to reduce towing-related wear and tear. What year is your Odyssey?
Unless it's undergone a recent full
renovation, there will certainly be issues with a 50 year old trailer. The biggest include rusted frames, worn out axles, and/or rotten floors. Broken or missing
windows can also be troublesome, because many older windows are no longer being made. And of course, wiring needs updating, appliances don't work...
If you're wanting to avoid a project, consider a newer
Scamp 13, something in the 5-15 year old range. Whatever the age, do a thorough pre-purchase inspection. Here's a tool you can download and print:
Buyer's Checklist