The collective flow of light nuclei is an important probe for understanding their production mechanisms in heavy-ion collisions. The STAR collaboration has reported that the atomic mass-number (A) scaling of light nuclei elliptic flow \(v_2\) breaks down at \(\sqrt{s_\text {NN}}= 3.0-3.9\) GeV. The observations reveal that, while protons maintain negative \(v_2\) values at mid-rapidity for both 3.0 and 3.2 GeV, light nuclei \(v_2\) exhibit a sign change from negative at 3.0 GeV to positive at 3.2 GeV. In this study, we investigate the \(v_2\) of protons and deuterons in mid-central Au+Au collisions at \(\sqrt{s_\text {NN}}=\) 3.0, 3.2, 3.5 and 3.9 GeV using the JAM2 microscopic transport model. Deuterons are formed via nucleon coalescence, with the spatial distance \(\Delta R\) and momentum difference \(\Delta P\) between constituent nucleons serving as the coalescence criteria. Our calculations reproduce the sign change in deuteron \(v_2\) at 3.2 GeV. We observe a pronounced dependence of the nucleon coalescence probability on the azimuthal angle relative to the reaction plane. This effect is primarily driven by the transverse momentum dependence of the mean spatial \(\langle \Delta R\rangle\) and momentum \(\langle \Delta P\rangle\) separations between nucleon pairs, which vary with the nucleon azimuthal angle. Moreover, our analysis indicates that the stiffness of the nuclear equation of state plays a crucial role in determining whether the sign change in deuteron \(v_2\) occurs near \(\sqrt{s_\text {NN}}=3.2\) GeV.
