  We investigate the origin of the extraplanar diffuse ionized gas (eDIG) and
its predominant ionization mechanisms in five nearby (17-46 Mpc) low-mass
($10^9\text{-}10^{10}$ $M_{\odot}$) edge-on disk galaxies: ESO 157-49, ESO
469-15, ESO 544-27, IC 217, and IC 1553. We acquired Multi Unit Spectroscopic
Explorer (MUSE) integral field spectroscopy and deep narrowband H$\alpha$
imaging of our sample galaxies. To investigate the connection between in-plane
star formation and eDIG, we perform a photometric analysis of our narrowband
H$\alpha$ imaging. We measure eDIG scale heights of $h_{z\text{eDIG}} = 0.59
\text{-} 1.39$ kpc and find a positive correlation between them and specific
star formation rates. In all galaxies, we also find a strong correlation
between extraplanar and midplane radial H$\alpha$ profiles. Using our MUSE
data, we investigate the origin of eDIG via kinematics. We find ionized gas
rotation velocity lags above the midplane with values between 10 and 27 km
s$^{-1}$ kpc$^{-1}$. While we do find hints of an accretion origin for the
ionized gas in ESO 157-49, IC 217, and IC 1553, overall the ionized gas
kinematics of our galaxies do not match a steady galaxy model or any simplistic
model of accretion or internal origin for the gas. We also construct standard
diagnostic diagrams and emission-line maps (EW(H$\alpha$), [NII]/H$\alpha$,
[SII]//H$\alpha$, [OIII]/H$\beta$) and find regions consistent with mixed OB
star and hot low-mass evolved stars (HOLMES) ionization, and mixed OB-shock
ionization. Our results suggest that OB stars are the primary driver of eDIG
ionization, while both HOLMES and shocks may locally contribute to the
ionization of eDIG to a significant degree. Despite our galaxies' similar
structures and masses, we find a surprisingly composite image of ionization
mechanisms and a multifarious origin for the eDIG.
