  The CH$^+$ ion is a key species in the initial steps of interstellar carbon
chemistry. Its formation in diverse environments where it is observed is not
well understood, however, because the main production pathway is so endothermic
(4280 K) that it is unlikely to proceed at the typical temperatures of
molecular clouds. We investigation CH$^+$ formation with the first
velocity-resolved spectral mapping of the CH$^+$ $J=1-0, 2-1$ rotational
transitions, three sets of CH $\Lambda$-doubled triplet lines, $^{12}$C$^+$ and
$^{13}$C$^+$, and CH$_3$OH 835~GHz E-symmetry Q branch transitions, obtained
with Herschel/HIFI over $\approx$12 arcmin$^2$ centered on the Orion BN/KL
source. We present the spatial morphologies and kinematics, cloud boundary
conditions, excitation temperatures, column densities, and $^{12}$C$^+$ optical
depths. Emission from C$^+$, CH$^+$, and CH is indicated to arise in the
diluted gas, outside of the explosive, dense BN/KL outflow. Our models show
that UV-irradiation provides favorable conditions for steady-state production
of CH$^+$ in this environment. Surprisingly, no spatial or kinematic
correspondences of these species are found with H$_2$ S(1) emission tracing
shocked gas in the outflow. We propose that C$^+$ is being consumed by rapid
production of CO to explain the lack of C$^+$ and CH$^+$ in the outflow, and
that fluorescence provides the reservoir of H$_2$ excited to higher
ro-vibrational and rotational levels. Hence, in star-forming environments
containing sources of shocks and strong UV radiation, a description of CH$^+$
formation and excitation conditions is incomplete without including the
important --- possibly dominant --- role of UV irradiation.
