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• Building a complete gas-gap heat switch model that covers the entire switching process. • Integrating activated carbon's adsorption characteristics into the theoretical model. • Designing the 4He gas-gap heat switch based on the model and testing its performance to validate the model. • Applying the gas-gap heat switch to a 4He sub-Kelvin sorption cooler and achieving a temperature of 773 mK. Gas-gap heat switches (GGHSs) are significant components in sub-Kelvin sorption coolers (SKSCs). To develop an effective GGHS for SKSCs, a complete GGHS theoretical model is proposed by integrating the adsorption characteristics of activated carbon and the principle of GGHSs. This model establishes a relationship between the temperature of activated carbon and the corresponding thermal conductance of GGHSs. Based on this model, a 4He GGHS was designed, which consists of two cylindrical copper blocks separated by a 0.2 mm gas gap and a surface area of 9.896 cm2. The device was charged with 100 kPa of 4He at 297 K. Near the base temperature of the GM cryocooler of 3 K, an ON thermal resistance of 20 K/W and an OFF thermal resistance of 21,650 K/W with 1 mW applied to the hot end were obtained, achieving a switching ratio of 1082.5. The experimental results were analyzed and compared with the theoretical data, and proved to be in good agreement. Finally, the GGHS was integrated with a SKSC, achieving an ultimate temperature of 773 mK. [ABSTRACT FROM AUTHOR]