Indeed, looking back on your previous observations, that is clear to me now. And when Physicist put the stamp of approval on the idea of odd numbered time dimensions so quickly, my first thought was "spin" (in a physics sense.)
The article may settle my curiosity from the physics side, but I am still wondering about the import of Minkowski space in higher dimension brane theory - or more specifically how calculable higher dimensional dynamics would be from a 4D worldview. I don't see how our current methods could "handle" it.
In sum, I still visualize the 4D timeline as a plane when viewed from an extra time dimension, and the full 4D as a block. Still pondering though…