To establish a more comprehensive understanding of the connection between galaxy mergers and active galactic nuclei (AGNs), it is essential to disentangle the contributions of intrinsic AGN luminosity and dust extinction to the merger-AGN connection. Since tidal features identified in deep images serve as direct evidence of recent mergers, we study the fraction of AGN hosts with tidal features (f_T_) for a large sample of 748 type 2 AGNs at z<0.063. Specifically, we examine f_T_ as a function of E(B-V), derived from the Balmer decrement, and the internal-extinction-corrected luminosity of the [OIII] {lambda}5007 emission line (L_[OIII]_), which is a proxy for bolometric AGN luminosity. Our main finding is that f_T_ is significantly higher only for AGNs that are simultaneously luminous and heavily dust-obscured. Specifically, AGNs with log L_[OIII]_>~41.5 and E(B-V)>~0.7 exhibit a high f_T_ of ~0.7. In contrast, AGNs with either low luminosity (log L_[OIII]<~41.0) or low dust obscuration (E(B-V)<~0.3) show a low f_T_ of <~0.2. This trend suggests that galaxy mergers preferentially trigger AGNs that are simultaneously luminous and dust-obscured, whereas AGNs that are either luminous but unobscured or dust-obscured but less luminous are not strongly associated with merger-driven triggering. Based on several assumptions, our result can also be interpreted, despite certain caveats, within the framework of a merger-initiated evolution model for AGNs, suggesting that AGNs that are both obscured and luminous are temporally closer to merger events than those with lower luminosity and less dust obscuration.