The mechanism of the time-delayed feedback and the auto-feedback signals of the coupled acceleration state on the resonance behavior of an auto-parametric dynamic vibration absorption pendulum structure under random loads is investigated. The third-order scale perturbation method is introduced to analyze the resonance responses in deterministic and random cases of the stochastic coupling auto-parametric dynamic vibration absorption pendulum system, as well as the critical criteria for determining the stability of vibration modes. Synchronously applying numerical simulation techniques to evaluate and simulate the resonance laws of the main and subsidiary vibration modes modulated by memory signals from multiple levels, including the deterministic amplitude-load response, the influence of the random load factor on the spatiotemporal trajectory of the system states, and the system random moment response. Further explore the characteristics of the deterministic moment solution varying with the load intensity, and clarify the evolution law of the system phase trajectory caused by bounded random loads formed by phase modulation based on the noise intensity factor. Besides, the random moments of system states maintain the phenomenon of main and subsidiary vibration modes through the modulation of main and internal resonances. Memory feedback signals cause the system vibration moments to exhibit periodicity and stability alternation, and system oscillation modes are sensitive to changes in the coupled memory feedback gain and this pattern leads to the system’s energy to be renewed. New ideas are developed in this paper for the stability design mode by the memory feedback signals modulation on the auto-parametric dynamic vibration absorption pendulum under random situations.