  Emission lines indicative of active accretion have been seen on a handful of
low-mass companions (M < 30 MJup) to stars. Line variability is ubiquitous on
stellar accretors but has never been characterized in detail on low-mass
companions and can give insights on the accretion mechanism at play. We
investigate the emission line variability of two low-mass companions (M<30
MJup) to stars to understand their accretion mechanisms. Using J-band
observations, we analyze the short to long-term variability of the HI Paschen
{\beta} emission line (1.282 {\mu}m) for GQ Lup b and GSC 06214-00210 b.
Archival spectroscopic observations are also examined to extend the time span.
We compare their line profiles and intensities to more massive accretors and
magnetospheric accretion and shock models. Both objects have HI Paschen {\beta}
flux variability that is moderate at short timescales (< 50 %) and increases at
longer timescales (~1000 % on decade timescales), resembling classical T Tauri
stars. GQ Lup b's line profiles are compatible with magnetospheric accretion.
GSC 06214-00210 b's profiles are reproduced by both magnetospheric accretion
and shock models, except for the brightest epoch for which the shock model is
highly favored. Both companions have C/O values broadly consistent with solar
values. While magnetospheric accretion is favored for GQ Lup b, higher
resolution (R > 10000) observations are required to disentangle the two
(non-exclusive) line formation mechanisms. The similarity in variability
behavior may support similar accretion mechanisms between these low-mass
companions and classical T Tauri stars. The significant variability observed at
months and longer timescales could explain the low yield of H{\alpha} imaging
campaigns.
