By using mass-separated sources, positrons as well as β-delayed protons and γ-rays were measured from the β-decay of 1 0 2 In (T 1 2 = 22 ± 1 s) and 1 0 0 In (T 1 2 = 6.1 ± 0.9 s). In particular, the average β + (β + + EC) ratio for the decay of 1 0 2 In was measured to be 0.76(4) and the level scheme of 1 0 2 Cd was extended. Whereas no direct β + EC feeding of the identified 1 0 2 Cd levels was observed, there is evidence for population of 1 0 2 Cd states at high excitation energy followed by statistical γ-decay. This feature, which has been deduced on the basis of the measured positron spectrum and the measured β + (β + + EC) ratio of the 1 0 2 In decay, is compared to the decay properties of the heavier odd-odd indium isotopes 1 0 4 In, 1 0 6 In and 1 0 8 In, and is also used to interpret the observed β-delayed proton data of 1 0 2 In and 1 0 0 In. For the first time, large-space shell-model calculations have been performed for the Gamow-Teller decay of heavy odd-odd nuclei. The decay results from these calculations are in good overall agreement with the gross decay properties of 1 0 2 In and 1 0 0 In deduced from the experiment.