  We prove that all the solutions of a quasi-periodically forced linear
Klein-Gordon equation $\psi_{tt}-\psi_{xx}+\mathtt{m}\psi+Q(\omega t)\psi=0 $
where $ Q(\omega t) := a^{(2)}(\omega t, x) \partial_{xx} + a^{(1)}(\omega t,
x)\partial_x + a^{(0)}(\omega t, x) $ is a differential operator of order $ 2
$, parity preserving and reversible, are almost periodic in time and uniformly
bounded for all times, provided that the coefficients $ a^{(2) }, a^{(1) },
a^{(0) } $ are small enough and the forcing frequency $\omega\in {\mathbb
R}^{\nu}$ belongs to a Borel set of asymptotically full measure. This result is
obtained by reducing the Klein-Gordon equation to a diagonal constant
coefficient system with purely imaginary eigenvalues. The main difficulty is
the presence in the perturbation $ Q (\omega t) $ of the second order
differential operator $ a^{(2)}(\omega t, x)\partial_{xx} $. In suitable
coordinates the Klein-Gordon equation is the composition of two
backward/forward quasi-periodic in time perturbed transport equations with
non-constant coefficients, up to lower order pseudo-differential remainders. A
key idea is to straighten this first order pseudo-differential operator with
bi-characteristics through a novel quantitative Egorov analysis.
