Cross Correlation, how can any signals except the trivial cases be uncorrelated?
Tl;DR version:  You are not missing anything; finite-duration signals cannot be uncorrelated signals.

If the crosscorrelation function $x\star y$ of $x$ and $y$ is zero everywhere, then the Fourier transform of $x\star y$, which is $X(f)Y^*(f)$ (or $X^*(f)Y(f)$ for left-handed folks), must also have value $0$ for all $f$. But, finite-duration signals have Fourier transforms with support $(-\infty, \infty)$
and so the product $X(f)Y^*(f)$ cannot be zero everywhere.

It is of course possible to have uncorrelated signals, but these have Fourier transforms with finite (and non-overlapping) support, and so (by duality) must have infinite duration.