Amorphous metal oxides with analog resistive switching functions (i.e., continuous controllability of the electrical resistance) are gaining emerging interest due to their neuromorphic functionalities promising for energy efficient electronics. The mechanisms are currently attributed to field-driven migration of the constituent ions, but the applications are being hindered by the limited understanding of the physical mechanisms due to the difficulty in analyzing the causal ion migration, which occurs on a nanometer or even atomic scale. Here, the direct electrical transport measurement of analog resistive switching and ångström scale imaging of the causal ion migration is demonstrated in amorphous TaOx (a-TaOx) by conductive atomic force microscopy. Atomically flat thin films of a-TaOx, which is a practical material for commercial resistive random access memory, are fabricated in this study, and the mechanisms of the three known types of analog resistive switching phenomena (current-dependent set, voltage-dependent reset, and time-dependent switching) are directly visualized on the surfaces. The observations indicate that highly analog type of resistive switching can be induced in a-TaOx by inducing the continuous redox reactions for 2.0 < x < 2.5, which are characteristic of a-TaOx. The measurements also demonstrate drastic control of the switching stochasticity, which is attributable to controlled segregation of a metastable a-TaO2 phase. The findings provide direct clues for tuning the analog resistive switching characteristics of amorphous metal oxides and developing new functions for future neuromorphic computing.