Interviews are a widely used technique in requirements elicitation to gather stakeholder needs, preferences, and expectations for a software system. Effective interviewing requires skilled interviewers to formulate proper interview questions in real time, while they face multiple challenges, including a lack of domain familiarity, excessive cognitive load and information overload that hinders how humans process stakeholder speech. Recently, large language models (LLMs) have exhibited state-of-the-art performance in multiple natural language processing tasks, including text summarization and entailment. To support interviewers, we investigate the application of GPT-4o to generate follow-up interview questions during requirements elicitation by building on a framework of common interviewer mistake types. In addition, we describe methods to generate questions based on interviewee speech, we report a controlled experiment to evaluate LLM-generated and human-authored questions with minimal guidance, and a second controlled experiment to evaluate the LLM-generated questions when generation is guided by interviewer mistake types. Our findings demonstrate that for both experiments, LLM-generated questions are no worse than human-authored questions with respect to clarity, relevancy and informativeness. Moreover, the LLM-generated questions outperform human-authored questions when guided by common mistake types. This highlights the potential of using LLMs to aid interviewers to enhance real-time interview requirements elicitation quality and ease.