So, since this original exchange, I made a simple Google Sites website and embedded a timeline.
The one change I had to make from the basic copy/paste operation was to change the beginning part of the "src" attribute in the iframe embed
From
To
That is,
To
Of course, what comes after the "?" in the src attribute will be unique to every Timeline.
It's not ideal, but it is hard to know how to change the embed generator to make it more clear when it only applies in some cases.
Best