  We investigate the connection between the most luminous active galactic
nuclei (AGN), galaxy pairs, and post-mergers in the IllustrisTNG simulation. We
select galaxy pairs and post-mergers with a mass ratio between 1:10 $< \mu <$
1:1 and a redshift between $0<z<1$. We compare the incidence of luminous AGN in
pairs with matched non-pair controls, finding that AGN with luminosity
$L_{\mathrm{bol}}>10^{44}$ erg/s occur in $\sim $26\% of paired galaxies with a
companion within 20 kpc, compared with $\sim $14\% in controls (a fractional
excess of $\sim$2). The enhancement of AGN in galaxy pairs is luminosity
dependent, with the highest excess (a factor of $\sim6\pm2$ at the closest
separations) for AGN with $L_{\mathrm{bol}}>10^{45}$ erg/s. Additionally, pairs
exhibit a modest yet statistically significant excess of luminous AGN up to
$\sim$150 kpc in separation. For pairs which merge between $0<z<1$, AGN
fractions are elevated between 1.5 Gyr before and after coalescence, with the
highest excess closest to coalescence. Our results indicate that
pre-coalescence interactions drive excesses of luminous AGN, but that luminous
AGN in galaxy pairs are not ubiquitous. Finally, we investigate what fraction
of AGN can be associated with an interaction (either having a companion within
100 kpc or a merger within the last 500 Myr). For AGN with
$L_{\mathrm{bol}}>10^{45}$ erg/s, $\sim$55\% are interacting, compared with a
30\% interaction fraction in AGN with $10^{44}<L_{\mathrm{bol}}<10^{44.5}$
erg/s. Our results support a picture in which interactions play a dominant role
in (but are not the sole cause of) triggering the most luminous AGN.
