The Longitudinal Valley Fault (LVF) and the Central Range Fault (CRF) in eastern Taiwan consist of a head-to-head double-vergence structure hosting disastrous earthquakes. It was previously proposed that the fault slip on one of these faults suppresses the earthquake generation on the other. Nonetheless, the 2022 Chihshang earthquake (Mw 7.0) on the CRF occurred soon after the 2022 Yuli earthquake (Mw 6.7) on the LVF. Here, we provide a comprehensive framework of the fault interaction consistently explaining these contradictory findings. First, we estimated the coseismic slip distribution of the Yuli earthquake from Global Navigation Satellite System (GNSS) and L-band satellite interferograms. The results indicate almost pure reverse faulting. Second, with the estimated slip distribution, we calculated changes in Coulomb failure function (ΔCFF) on the CRF due to the Yuli earthquake on the LVF. The ΔCFF reaches +0.25 MPa around the main rupture area of the Chihshang earthquake, which is equivalent to the clock advance of ~50 years, suggesting a large impact on the earthquake generation cycles. Finally, we found that a rake angle of fault slip has a significant effect on the ΔCFF on the other fault in the double-vergence structure: it takes large positive values when 90° like the Yuli earthquake, but almost negative when 45° or less, which comprehensively explains the seismic quiescence previously reported and the positive ΔCFF on the CRF caused by the Yuli earthquake. The strong impact of the rake angle is also supported by the temporal distribution of historical earthquakes in eastern Taiwan.