We revisit a classic study [D. S. Hall et al., Phys. Rev. Lett. 81, 1539 (1998)] of interpenetrating Bose-Einstein condensates in the hyperfine states |F=1,mf=-1⟩≡|1⟩ and |F=2,mf=+1⟩≡|2⟩ of 87Rb 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).