Recently, the T-hetero-nuclear multiple quantum coherence (T-HMQC) sequence using the TRAPDOR (transfer of population in double resonance) recoupling has been introduced for the indirect detection via protons of quadrupolar nuclei with spin I = 1 (14N) or 3/2 (35Cl) in solids at fast magic-angle spinning (MAS). The sequence is simple as it only uses four rectangular pulses and exhibits low t1-noise because the recoupling pulses are applied to the indirectly detected isotope, I. We demonstrate that this sequence is applicable for the detection via protons of spin-1/2 nuclei subject to large chemical shift anisotropy, such as 195Pt. We also report the proton detection of double-quantum (2Q) coherences of 14N nuclei using this sequence. This 2Q version is more robust to the adjustment of the magic angle and the instabilities of the MAS frequencies than its parent single-quantum (1Q) version since the 2Q coherences are not broadened by the first-order quadrupole interaction. In practice, than its 1Q counterpart for the indirect detection of 14N nuclei, the 2Q variant benefits from a slightly higher resolution and comparable sensitivity. In this article, we derive for the first time the Hamiltonian that describes the spin dynamics during the TRAPDOR recoupling. This Hamiltonian demonstrates the importance of the adiabaticity parameter as well as the role of third-order terms in the effective Hamiltonian. The effects of offsets, radio-frequency field, and recoupling time on the efficiency of the T-HMQC sequence are analyzed numerically as well as with experimental detection via protons of 195Pt nuclei in a mixture of cis- and trans-platin and that of 14N and 35Cl isotopes in l-histidine HCl.