Neutrino signals in electron-capture decays of hydrogen-like parent ions P in storage-ring experiments at GSI are reconsidered, with special emphasis placed on the storage-ring quasi-circular motion of the daughter ions D in two-body decays P --> D + e-neutrino. It is argued that to the extent that daughter ions are detected, these detection rates might exhibit modulations with periods of order seconds, similar to those reported in the GSI storage-ring experiments for two-body decay rates [1,2]. New dedicated experiments in storage rings, or using traps, could explore these modulations.