  The spectrum and dynamical instability, as well as the transient effect of
the tensor perturbation for the so-called Maeda-Dadhich black hole, a type of
Kaluza-Klein black hole, in Einstein-Gauss-Bonnet gravity have been
investigated in framework of pseudospectrum. We cast the problem of solving
quasinormal modes (QNMs) in AdS-like spacetime as the linear evolution problem
of the non-normal operator in null slicing by using ingoing
Eddington-Finkelstein coordinates. In terms of spectrum instability, based on
the generalised eigenvalue problem, the QNM spectrum and
$\epsilon$-pseudospectrum has been studied, while the open structure of
$\epsilon$-pseudospectrum caused by the non-normality of operator indicates the
spectrum instability. In terms of dynamical instability, the concept of the
distance to dynamical instability has been firstly introduced in gravity
aspects, which plays a crucial role in bridging the spectrum instability and
the dynamical instability. We calculate the distance, named the complex
stability radius, as parameters vary. Finally, we report the transient effect
in the energy norm of the evolution operator, whose behaviour can be roughly
reflected by the three kinds of abscissas in context of pseudospectrum, and
explain the relationship between the waveform and the transient effect.
