Precise understanding of the spatiotemporal characteristics of plasmons is essential for the development of applications of plasmonic nanoparticles. In this study, we investigated the spatiotemporal properties of high-order plasmon modes induced in a gold triangular nanoplate by static and dynamic near-field measurements. The near-field transmission measurements revealed that in-plane and out-of-plane polarized plasmon modes were simultaneously excited and these modes spectroscopically and spatially overlapped. The superposition of these modes was visualized in the near-field two-photon excitation image of the nanoplate. We performed time-resolved autocorrelation measurements on the nanoplate and found that the correlation width was broader than the excitation pulse due to the plasmon dephasing process. From the correlation width map of the nanoplate, we experimentally demonstrated that the out-of-plane plasmon mode exhibits a longer dephasing time than the in-plane plasmon mode. These findings indicate that the out-of-plane mode is desirable for improving the performance of plasmons in various applications.