The full sequence of the bound states for a very floppy triatomic complex, Ne2H- in its ground electronic state, are initially computed for the rotationless situation and employing a variational approach that expands the total nuclear wave function over a large set of symmetry-adapted, distributed Gaussian functions and employs accurate atom-atom potential energy data. The results are tested for numerical convergence, compared with the behavior of both its diatomic fragments, Ne-2 and NeH-, and further compared with the results for the Ne-3 case. The computational analysis is extended to the production of the rotational constants for the very nonclassical ground state vibrational configuration by making use of the previous findings. The method is shown to provide us with several illuminating details on the nanoscopic internal dynamics of this very weakly bound quantum aggregate.