The A dependence of the forward cross section for inclusive pion double charge exchange on nine target nuclei from 6Li to 209Bi at T0 = 0.59 GeV, as well as the cross section for 6Li, 7Li, and 12C nuclei at T0 = 0.59, 0.75, and 1.1 GeV, was measured with the 3-m magnetic spectrometer of the Institute of Theoretical and Experimental Physics (ITEP, Moscow). The resulting A dependence is well described within the model involving two sequential single charge exchanges and taking into account the renormalization of the amplitude for pion single charge exchange in a nucleus. A relatively weak energy dependence of the cross section for the 6Li, 7Li, and 12C nuclei agrees with the analogous dependence obtained previously for the 16O nucleus, but it contradicts the predicted sharp decrease in the cross section within the model involving two sequential single charge exchanges. This result provides an additional piece of evidence that the contribution from the mechanism of inelastic Glauber rescattering is significant at T0 ≳ 0.6 GeV.