The correlated Tunneling Transfer Ionization (TuTI) channel in fast 4-body processes p+He→H⁰+He²⁺+e is utilized to probe the highly correlated asymptotic parts of the He ground-state momentum space wave function. In this reaction, predominantly at large nuclear impact parameters, one electron in the He ground state is captured by the proton by tunneling through the two-center barrier when electron and proton velocity vectors resonantly match. The measured 3-particle final-state momentum distributions show characteristic features that we trace back to the highly correlated non-s² components of the He ground-state momentum wave function. This conclusion is supported by a simple heuristic model.