This is backwards, immigration will grant a visa to a teacher with no degree provided that teacher is a native speaker and have 3 years teaching experience.

The longer you postpone getting a degree, the less likely it is you'll ever do so. So just get a degree, then come to Japan if the idea still appeals.

What is a 'degree'?
 

I am 40 and lived in the US all my life. I have a Bachelors Degree is Marketing, but not in teaching. Would I need a teaching degree to be able to find a job teaching English in Japan?

After a recent trip to Japan as a tourist, I am interested in spending more time there. I am divorced so it's only me.

Any advice would be appreciated.

Not at all. The only requirement for english teaching schools is a Bachelors degree which you have - you will be fine! You just will need to find an english teaching school to sponsor you if you are hoping to stay out there for more than 3 months.
Unfortunately you just miss out on eligibility for the JET programme (cannot be older than 39), so thats a bit of a bugger eh.