A well-known approach to the self-dynamics of liquids is based on the Gaussian approximation, where it is assumed that the motion of a molecule is fully determined by a unique function of time directly related to the velocity auto-correlation function. Experimental inquiries into the presence of non-Gaussian dynamics are still scarce, particularly concerning low-temperature liquids exhibiting moderate quantum effects (i.e. H2, D2, and Ne). Though experimental evidences of the breakdown of the Gaussian approximation in liquid para-H2 (and in its isotopic mixtures with D2) have been recently obtained by the present authors, the density behavior of this phenomenon and its link with the self-diffusion coefficient are not completely understood. These two issues will be tackled by a new neutron investigation on three liquid para-H2/Ne mixtures exhibiting various hydrogen concentrations.