Generative Social Agents (GSAs) are increasingly impacting human users through persuasive means. On the one hand, they might motivate users to pursue personal goals, such as healthier lifestyles. On the other hand, they are associated with potential risks like manipulation and deception, which are induced by limited control over probabilistic agent outputs. However, as GSAs manifest communicative patterns based on available knowledge, their behavior may be regulated through their access to such knowledge. Following this approach, we explored persuasive ChatGPT-generated messages in the context of human-robot physiotherapy motivation. We did so by comparing ChatGPT-generated responses to predefined inputs from a hypothetical physiotherapy patient. In Study 1, we qualitatively analyzed 13 ChatGPT-generated dialogue scripts with varying knowledge configurations regarding persuasive message characteristics. In Study 2, third-party observers (N = 27) rated a selection of these dialogues in terms of the agent's expressiveness, assertiveness, and persuasiveness. Our findings indicate that LLM-based GSAs can adapt assertive and expressive personality traits -- significantly enhancing perceived persuasiveness. Moreover, persuasiveness significantly benefited from the availability of information about the patients' age and past profession, mediated by perceived assertiveness and expressiveness. Contextual knowledge about physiotherapy benefits did not significantly impact persuasiveness, possibly because the LLM had inherent knowledge about such benefits even without explicit prompting. Overall, the study highlights the importance of empirically studying behavioral patterns of GSAs, specifically in terms of what information generative AI systems require for consistent and responsible communication.