As globular clusters (GCs) orbit the Milky Way, their stars are tidally stripped and form tidal tails that follow the orbit of the cluster around the Galaxy. The morphology of these tails is complex and shows correlations with the phase of orbit and the orbital angular velocity, especially for GCs on eccentric orbits. Here we focus on two GCs, NGC 1261 and NGC 1904, that were potentially accreted alongside Gaia-Enceladus and that have shown signatures of having, in addition to tidal tails, structures formed by distributions of extra-tidal stars that are misaligned with the general direction of the clusters'respective orbits. To provide an explanation for the formation of these structures, we made use of spectroscopic measurements from the Southern Stellar Stream Spectroscopic Survey (S5) as well as proper motion measurements from Gaia's third data release (DR3), and applied a Bayesian mixture modelling approach to isolate high-probability member stars. We recovered extra-tidal features surrounding each cluster matching findings from previous work. We then conducted N-body simulations and compared the expected spatial distribution and variation in the dynamical parameters along the orbit with those of our potential member sample. Furthermore, we used Dark Energy Camera (DECam) photometry to inspect the distribution of the member stars in the colour-magnitude diagram (CMD). We find that potential members agree reasonably with the N-body simulations, and that the majority follow a simple stellar population distribution in the CMD, which is characteristic of GCs. We link the extra-tidal features with their orbital properties and find that the presence of the tails agrees well with the theory of stellar stream formation through tidal disruption. In the case of NGC 1904, we clearly detect the tidal debris escaping the inner and outer Lagrange points, which are expected to be prominent when at or close to the apocentre of its orbit. Our analysis allows for further exploration of other GCs in the Milky Way that exhibit similar extra-tidal features.