  Low mass galaxy pair fractions are understudied, and it is unclear whether
low mass pair fractions evolve in the same way as more massive systems over
cosmic time. In the era of JWST, Roman, and Rubin, selecting galaxy pairs in a
self-consistent way will be critical to connect observed pair fractions to
cosmological merger rates across all mass scales and redshifts. Utilizing the
Illustris TNG100 simulation, we create a sample of physically associated low
mass ($\rm 10^8<M_*<5\times10^9\,M_\odot$) and high mass ($\rm
5\times10^9<M_*<10^{11}\,M_\odot$) pairs between $z=0$ and $4.2$. The low mass
pair fraction increases from $z=0$ to $2.5$, while the high mass pair fraction
peaks at $z=0$ and is constant or slightly decreasing at $z>1$. At $z=0$, the
low mass major (1:4 mass ratio) pair fraction is 4$\times$ lower than high mass
pairs, consistent with findings for cosmological merger rates. We show that
separation limits that vary with the mass and redshift of the system, such as
scaling by the virial radius of the host halo ($r_{\mathrm{sep}}< 1 R_{\rm
vir}$), are critical for recovering pair fraction differences between low mass
and high mass systems. Alternatively, static physical separation limits applied
equivalently to all galaxy pairs do not recover the differences between low and
high mass pair fractions, even up to separations of $300$ kpc. Finally, we
place isolated mass-analogs of Local Group galaxy pairs, i.e., Milky Way
(MW)--M31, MW--LMC, LMC--SMC, in a cosmological context, showing that isolated
analogs of LMC--SMC-mass pairs and low-separation ($<50$ kpc) MW--LMC-mass
pairs are $2-3\times$ more common at $z\gtrsim2-3$.
