Question about "2-dimensional time"?

You've invented a unit (sec²) in the "duration" example, haven't given an example of anything real that you can measure with that unit.  So how is this explaining "what '2-dimensional' [time] would be like"?

As for the date coordinates, you didn't explain what you meant by "X", but if it's conventional multiplication then that's not now spatial coordinates work.  You don't use area as a unit for specifying a position in a plane or volume for position in 3-space.  You use ordered pairs or triples of length measurements for Cartesian coordinates; and you use some combination of lengths and angles for polar, cylindrical or spherical coordinates.  

There's not much use for the product of spatial coordinates anyway, since that product can always be made zero by a choice of origin where one coordinate is zero.  When you do multiply, the factors tend to be things that *don't* depend on the choice of a coordinate system.  The radius of a given sphere doesn't change when you mvoe the spatial origin to another point, so the r in V = 4πr³ / 3 is not a spatial coordinate, but the magnitude of the displacement from the center to some point on the surface of the sphere. 

I'm not trying to step on your creativity.  It's just that if you have a serious idea that's substantially different from established practice, you'll have to do a better job of explaining why it's worthwhile.

[If this is for science fiction, though, any sensible-sounding technobabble will do. :^)]

Consider a spacetime diagram. The X and Y axes are space and z is time. (One space direction is not shown) A world-line of an object shows how it moves thru space as it goes up the z axis which represents moving in time. This is a static unchanging model. But if there was a 2nd time dimension, the world-line would move and wiggle around. 

This means our past would constantly be changing. A roll of dice in the present could give many different results at the same time. An object could be in many places at the same time. 

Many different timelines, all parallel to each other, would form a 2 dimensional time plane. If you could move thru the 2nd time direction, you could keep changing timelines. 

Have you talked to a doctor about your delusions?

my idea is that you dropped some DMT .