  For a given centered Gaussian process with stationary increments $\{X(t),
t\geq 0\}$ and $c>0$, let $$ W_\gamma(t)=X(t)-ct-\gamma\inf_{0\leq s\leq
t}\left(X(s)-cs\right), \quad t\geq 0$$ denote the $\gamma$-reflected process,
where $\gamma\in (0,1)$. This process is introduced in the context of risk
theory to model surplus process that include tax payments of loss-carry forward
type.In this contribution we derive asymptotic approximations of both the ruin
probability and the joint distribution of first and last passage times given
that ruin occurs. We apply our findings to the cases with $X$ being the
multiplex fractional Brownian motion and the integrated Gaussian processes. As
a by-product we derive an extension of Piterbarg inequality \KD{for}
threshold-dependent random fields.
