As software systems grow increasingly complex, explainability has become a crucial non-functional requirement for transparency, user trust, and regulatory compliance. Eliciting explainability requirements is challenging, as different methods capture varying levels of detail and structure. This study examines the efficiency and effectiveness of three commonly used elicitation methods—focus groups, interviews, and online surveys—while also assessing the role of taxonomy usage in structuring and improving the elicitation process. We conducted a case study at a large German IT consulting company, utilizing a web-based personnel management software. A total of two focus groups, 18 interviews, and an online survey with 188 participants were analyzed. The results show that interviews were the most efficient, capturing the highest number of distinct needs per participant per time spent. Surveys collected the most explanation needs overall but had high redundancy. Delayed taxonomy introduction resulted in a greater number and diversity of needs, suggesting that a two-phase approach is beneficial. Based on our findings, we recommend a hybrid approach combining surveys and interviews to balance efficiency and coverage. Future research should explore how automation can support elicitation and how taxonomies can be better integrated into different methods.