  Since the discovery of $z\sim 6$ quasars two decades ago, studies of their
Ly$\alpha$-transparent proximity zones have largely focused on their utility as
a probe of cosmic reionization. But even when in a highly ionized intergalactic
medium, these zones provide a rich laboratory for determining the timescales
that govern quasar activity and the concomitant growth of their supermassive
black holes. In this work, we use a suite of 1D radiative transfer simulations
of quasar proximity zones to explore their time-dependent behaviour for
activity timescales from $\sim10^3$ to $10^8$ years. The sizes of the simulated
proximity zones, as quantified by the distance at which the smoothed Ly$\alpha$
transmission drops below 10% (denoted $R_p$), are in excellent agreement with
observations, with the exception of a handful of particularly small zones that
have been attributed to extremely short $\lesssim 10^4$ year lifetimes. We
develop a physically motivated semi-analytic model of proximity zones which
captures the bulk of their equilibrium and non-equilibrium behaviour, and use
this model to investigate how quasar variability on $\lesssim10^5$ year
timescales is imprinted on the distribution of observed proximity zone sizes.
We show that large variations in the ionizing luminosity of quasars on
timescales of $\lesssim10^4$ years are disfavored based on the good agreement
between the observed distribution of $R_p$ and our model prediction based on
"lightbulb" (i.e. steady constant emission) light curves.
