Monitoring mass accretion onto substellar objects provides insights into the geometry of the accretion flows. We use the Lulin One-meter Telescope to monitor H{alpha} emission from FUTauB, a ~19MJup brown-dwarf companion at 5.7" (719au) from the host star, for six consecutive nights. This is the longest continuous H{alpha} monitoring for a substellar companion near the deuterium-burning limit. We aim to investigate if accretion near the planetary regime could be rotationally modulated as suggested by magnetospheric accretion models. We find tentative evidence that H{alpha} mildly varies on hourly and daily timescales, though our sensitivity is not sufficient to definitively establish any rotational modulation. No burst-like events are detected, implying that accretion onto FUTauB is overall stable during the time baseline and sampling windows over which it was observed. The primary star FUTauA also exhibits H{alpha} variations over timescales from minutes to days. This program highlights the potential of monitoring accretion onto substellar objects with small telescopes.