A detailed analysis of magneto-optical Zeeman data for the dominating trigonal complex defect in Ag-diffused ZnTe, with a bound exciton (BE) at 2.3149 eV, is presented. The electronic structure of this BE can be explained in a satisfactory way assuming a neutral (isoelectronic) defect, where both electron and hole wave functions are rather localized, approximately leading to a triplet BE configuration at lowest energy. The strong 2.3149-eV line corresponds to a MS=1 doublet of this triplet. The electron is rather strongly localized, with an isotropic g value ge=+0.55, quite different from the value for shallow donors in ZnTe (ge=-0.40). This conclusion is also supported by the low value of the quadratic Zeeman shift rate for the MS1 doublet, C=3.5×10-3 meV/T2. The hole is also rather strongly localized, and is approximately spinlike, but with a strong residual angular momentum &=2.70, &=1.20, with reference to the trigonal defect axis. This is consistent with the assumed identity of the defect: a trigonal pair AgZn-Agi, where AgZn is a moderately deep substitutional acceptor, and Agi is a deep donor, presumably at a tetrahedral interstitial site.