  We give examples of reducible characteristic cycles for irreducible
Harish-Chandra modules for $\mathrm{U}(p,q)$ by analyzing a four-dimensional
singular subvariety of $\mathbb{C}^8$. We relate this singularity to the
Kashiwara-Saito singularity arising for Schubert varieties for
${\mathrm{GL}}(8,\mathbb{C})$ with reducible characteristic cycles, as well as
recent related examples of Williamson. In particular, this gives another
explanation of the simple highest weight modules for
${\mathfrak{g}}{\mathfrak{l}}(12,\mathbb{C})$ with reducible associated
varieties that Williamson discovered.
