The condensation of magnetic quasiparticles into the nonmagnetic ground state has been used to explain novel magnetic ordering phenomena observed in quantum spin systems. We present neutron scattering results across the pressure-induced quantum phase transition and for the novel ordered phase of the magnetic insulator , which are consistent with the theoretically predicted two degenerate gapless Goldstone modes, similar to the low-energy spin excitations in the field-induced case. These novel experimental findings complete the field-induced Bose-Einstein condensate picture and support the recently proposed field-pressure phase diagram common for quantum spin systems with an energy gap of singlet-triplet nature.