This study explores the application of generative AI (GenAI) within manual exploitation and privilege escalation tasks in Linux-based penetration testing environments, two areas critical to comprehensive cybersecurity assessments. Building on previous research into the role of GenAI in the ethical hacking lifecycle, this paper presents a hands-on experimental analysis conducted in a controlled virtual setup to evaluate the utility of GenAI in supporting these crucial, often manual, tasks. Our findings demonstrate that GenAI can streamline processes, such as identifying potential attack vectors and parsing complex outputs for sensitive data during privilege escalation. The study also identifies key benefits and challenges associated with GenAI, including enhanced efficiency and scalability, alongside ethical concerns related to data privacy, unintended discovery of vulnerabilities, and potential for misuse. This work contributes to the growing field of AI-assisted cybersecurity by emphasising the importance of human-AI collaboration, especially in contexts requiring careful decision-making, rather than the complete replacement of human input.