From observations of almost 500 red giant branch stars in 29 Galactic open and globular clusters, we have investigated the behavior of the infrared Ca II triplet (8498, 8542, and 8662 Å) in the age range 13 Gyr <= age <= 0.25 Gyr and the metallicity range -2.2 <= [Fe/H] <= +0.47. These are the widest ranges of ages and metallicities in which the behavior of the Ca II triplet lines has been investigated in a homogeneous way. We report the first empirical study of the variation of the Ca II triplet lines' strength, for given metallicities, with respect to luminosity. We find that the sequence defined by each cluster in the luminosity-ΣCa plane is not exactly linear. However, when only stars in a small magnitude interval are observed, the sequences can be considered as linear. We have studied the Ca II triplet lines on three metallicity scales. While a linear correlation between the reduced equivalent width (W or W) and metallicity is found in the Carretta & Gratton and Kraft & Ivans scales, a second-order term needs to be added when the Zinn & West scale is adopted. We investigate the role of age from the wide range of ages covered by our sample. We find that age has a weak influence on the final relationship. Finally, the relationship derived here is used to estimate the metallicities of three poorly studied open clusters: Berkeley 39, Trumpler 5, and Collinder 110. For the latter, the metallicity derived here is the first spectroscopic estimate available.