  We consider the asymmetric simple exclusion process on $\mathbb{Z}$ with a
single second class particle initially at the origin. The first class particles
form two rarefaction fans which come together at the origin, where the large
time density jumps from $0$ to $1$. We are interested in $X(t)$, the position
of the second class particle at time $t$. We show that, under the KPZ $1/3$
scaling, $X(t)$ is asymptotically distributed as the difference of two
independent, $\mathrm{GUE}$-distributed random variables.The key part of the
proof is to show that $X(t)$ equals, up to a negligible term, the difference of
a random number of holes and particles, with the randomness built up by ASEP
itself. This provides a KPZ analogue to the 1994 result of Ferrari and Fontes
\cite{FF94b}, where this randomness comes from the initial data and leads to
Gaussian limit laws.
