We revisit a classic study [D. S. Hall , Phys. Rev. Lett. 81, 1539 (1998)PRLTAO0031-900710.1103/PhysRevLett.81.1539] of interpenetrating Bose-Einstein condensates in the hyperfine states and of and observe striking new nonequilibrium component separation dynamics in the form of oscillating ringlike structures. The process of component separation is not significantly damped, a finding that also contrasts sharply with earlier experimental work, allowing a clean first look at a collective excitation of a binary superfluid. We further demonstrate extraordinary quantitative agreement between theoretical and experimental results using a multicomponent mean-field model with key additional features: the inclusion of atomic losses and the careful characterization of trap potentials (at the level of a fraction of a percent).