= Solution
Subtract the background <hydrostatic pressure>. A relief amplitude $h$ produces a restoring <pressure> perturbation $p'\sim\rho gh$ and horizontal <gradient> $\rho gh/\lambda$. <Incompressibility> makes the disturbance penetrate a depth of order its horizontal scale. For <sinusoidal viscous rebound>, with relaxation <speed> $v\sim h/\tau$, the viscous <force density> is $\eta v/\lambda^2$. Balancing gives
$$
\eta\frac{h}{\tau\lambda^2}\sim\frac{\rho gh}{\lambda},
\qquad\boxed{\tau\sim\frac{\eta}{\rho g\lambda}.}
$$
This is a small-amplitude viscous half-space estimate; numerical factors from the sinusoidal geometry are absent from a scaling argument.
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