Regions of rapid variation in the internal structure of a star are often referred to as acoustic glitches since they create a characteristic periodic signature in the frequencies of p modes. Here we examine the localized disturbance arising from the helium second ionization zone in red giant branch and clump stars. More specifically, we determine how accurately and precisely the parameters of the ionization zone can be obtained from the oscillation frequencies of stellar models. We use models produced by three different generation codes that not only cover a wide range of stages of evolution along the red giant phase but also incorporate different initial helium abundances. To study the acoustic glitch caused by the second ionization zone of helium we have determined the second differences in frequencies of modes with the same angular degree, l, and then we fit the periodic function described by Houdek & Gough to the second differences. We discuss the conditions under which such fits robustly and accurately determine the acoustic radius of the second ionization zone of helium. When the frequency of maximum amplitude of the p-mode oscillations was greater than 40 μHz a robust value for the radius of the ionization zone was recovered for the majority of models. The determined radii of the ionization zones as inferred from the mode frequencies were found to be coincident with the local maximum in the first adiabatic exponent described by the models, which is associated with the outer edge of the second ionization zone of helium. Finally, we consider whether this method can be used to distinguish stars with different helium abundances. Although a definite trend in the amplitude of the signal is observed any distinction would be difficult unless the stars come from populations with vastly different helium abundances or the uncertainties associated with the fitted parameters can be reduced. However, application of our methodology could be useful for distinguishing between different populations of red giant stars in globular clusters, where distinct populations with very different helium abundances have been observed.