  The time variability and spectra of directly imaged companions provide
insight into their physical properties and atmospheric dynamics. We present
follow-up R~40 spectrophotometric monitoring of red companion HD 1160 B at
2.8-4.2 $\mu$m using the double-grating 360{\deg} vector Apodizing Phase Plate
(dgvAPP360) coronagraph and ALES integral field spectrograph on the Large
Binocular Telescope Interferometer. We use the recently developed technique of
gvAPP-enabled differential spectrophotometry to produce differential light
curves for HD 1160 B. We reproduce the previously reported ~3.2 h periodic
variability in archival data, but detect no periodic variability in new
observations taken the following night with a similar 3.5% level precision,
suggesting rapid evolution in the variability of HD 1160 B. We also extract
complementary spectra of HD 1160 B for each night. The two are mostly
consistent, but the companion appears fainter on the second night between
3.0-3.2 $\mu$m. Fitting models to these spectra produces different values for
physical properties depending on the night considered. We find an effective
temperature T$_{\text{eff}}$ = 2794$^{+115}_{-133}$ K on the first night,
consistent with the literature, but a cooler T$_{\text{eff}}$ =
2279$^{+79}_{-157}$ K on the next. We estimate the mass of HD 1160 B to be
16-81 M$_{\text{Jup}}$, depending on its age. We also present R = 50,000
high-resolution optical spectroscopy of host star HD 1160 A obtained
simultaneously with the PEPSI spectrograph. We reclassify its spectral type to
A1 IV-V and measure its projected rotational velocity v sin i = 96$^{+6}_{-4}$
km s$^{-1}$. We thus highlight that gvAPP-enabled differential
spectrophotometry can achieve repeatable few percent level precision and does
not yet reach a systematic noise floor, suggesting greater precision is
achievable with additional data or advanced detrending techniques.
