Context. Hot atomic hydrogen emission lines in pre-main sequence stars serve as tracers for physical processes in the innermost regions of circumstellar accretion disks, where the interaction between a star and disk is the dominant influence on the formation of infalls and outflows. In the highly magnetically active T Tauri stars, this interaction region is particularly shaped by the stellar magnetic field and the associated magnetosphere, covering the inner five stellar radii around the central star. Even for the closest T Tauri stars, a region as compact as this is only observed on the sky plane at sub-mas scales. To resolve it spatially, the capabilities of optical long baseline interferometry are required. Aims. We aim to spatially and spectrally resolve the Brγ hydrogen emission line with the methods of interferometry in order to examine the kinematics of the hydrogen gas emission region in the inner accretion disk of a sample of solar-like young stellar objects. The goal is to identify trends and categories among the sources of our sample and to discuss whether or not they can be tied to different origin mechanisms associated with Brγ emission in T Tauri stars, chiefly and most prominently magnetospheric accretion. Methods. We observed a sample of seven T Tauri stars for the first time with VLTI GRAVITY, recording spectra and spectrally dispersed interferometric quantities across the Brγ line at 2.16 µm in the near-infrared K-band. We used the visibilities and differential phases to extract the size of the Brγ emission region and the photocentre shifts on a channel-by-channel basis, probing the variation of spatial extent at different radial velocities. To assist in the interpretation, we also made use of radiative transfer models of magnetospheric accretion to establish a baseline of expected interferometric signatures if accretion is the primary driver of Brγ emission. Results. From among our sample, we find that five of the seven T Tauri stars show an emission region with a half-flux radius in the four to seven stellar radii range that is broadly expected for magnetospheric truncation. Two of the five objects also show Brγ emission primarily originating from within the co-rotation radius, which is an important criterion for magnetospheric accretion. Two objects exhibit extended emission on a scale beyond 10 R * , one of them is even beyond the K-band continuum half-flux radius of 11.3 R * . The observed photocentre shifts across the line can be either similar to what is expected for disks in rotation or show patterns of higher complexity. Conclusions. Based on the observational findings and the comparison with the radiative transfer models, we find strong evidence to suggest that for the two weakest accretors in the sample, magnetospheric accretion is the primary driver of Brγ radiation. The results for the remaining sources imply either partial or strong contributions coming from additional, spatially extended emission components in the form of outflows, such as stellar or disk winds. We expect that in ...