What's the purpose of a second dimension of time in physics in layman terms?
Speculative theories with more than one time dimension have been explored in physics. The additional dimensions may be similar to conventional time, compactified like the additional spatial dimensions in string theory or components of a complex time.
Based on the special orthogonal group $SO(10,2)$, representing the GUT spin group of the extended supersymmetry structure of M-theory, a "two-time physics" has been suggested.
F-theory describes a 12-dimensional spacetime having two time dimensions, giving it the metric signature (10,2).
The existence of a well-posed initial value problem for the ultrahyperbolic equation (a wave equation in more than one time dimension) demonstrates that initial data on a mixed (spacelike and timelike) hypersurface, obeying a particular nonlocal constraint, evolves deterministically in the remaining time dimension.
Like other Complex number variables, complex time is two-dimensional, comprising one real time dimension and one imaginary time dimension, changing time from a real number line into a complex plane. Introducing it into Minkowski spacetime allows a generalization of Kaluza–Klein theory.
Now, from a layman perspective, it's difficult to understand what was said. So I am wondering if a second time dimension is something real or potentially real and what the second time dimension would imply about the nature of time, because to me it seems that this second dimension is not real and would just be used to formalize something mathematically to make the reality fit into a particular theory.