  We present a lookdown construction for a Moran seed-bank model with variable
active and inactive population sizes and we show that the empirical measure of
our model coincides with that of the Seed-Bank-Moran Model with latency of
Greven, den Hollander and Oomen, 2022. Furthermore, we prove that the time to
the most recent common ancestor, starting from $N$ individuals with stationary
distribution over its state (active or inactive), has the same asymptotic order
as the largest inactivity period. We then obtain an asymptotic distribution of
the TMRCA, and use this result to find the first order of the asymptotic
distribution of the fixation time of a single beneficial mutant conditioned to
invade the whole population, which surprisingly is of order $\ln(N)$.
