We present MeerKAT Fornax Survey H I observations of NGC 1427A, a blue irregular galaxy with a stellar mass of ∼2 × 109 M⊙ located near the centre of the Fornax galaxy cluster. Thanks to the excellent resolution (1–6 kpc spatially, 1.4 km s−1 in velocity) and H I column density sensitivity (∼4 × 1019 to ∼1018 cm−2 depending on resolution), our data deliver new insights on the long-debated interaction of this galaxy with the cluster environment. We confirm the presence of a broad, one-sided, starless H I tail stretching from the outer regions of the stellar body and pointing away from the cluster centre. We find the tail to have 50% more H I (4 × 108 M⊙) and to be 3 times longer (70 kpc) than in previous observations. In fact, we detect scattered H I clouds out to 300 kpc from the galaxy in the direction of the tail – possibly the most ancient remnant of the passage of NGC 1427A through the intracluster medium of Fornax. Both the velocity gradient along the H I tail and the peculiar kinematics of H I in the outer region of the stellar body are consistent with the effect of ram pressure given the line-of-sight motion of the galaxy within the cluster. However, several properties cannot be explained solely by ram pressure and suggest an ongoing tidal interaction. This includes: the close match between dense H I and stars within the disturbed stellar body; the abundant kinematically anomalous H I; and the inversion of the H I velocity gradient near the base of the H I tail. We rule out an interaction with the cluster tidal field, and conclude that NGC 1427A is the result of a high-speed galaxy encounter or of a merger started at least 300 Myr ago, where ram pressure shapes the distribution and kinematics of the H I in the perturbed outer stellar body and in the tidal tails.