Trust in digital systems depends on secure hardware, often assured through Hardware Reverse Engineering (HRE). This work develops methods for investigating human problem-solving processes in HRE, an underexplored yet critical aspect. Since reverse engineers rely heavily on visual information, eye tracking holds promise for studying their cognitive processes. To gain further insights, we additionally employ verbal thought protocols during and immediately after HRE tasks: Concurrent and Retrospective Think Aloud. We evaluate the combination of eye tracking and Think Aloud with 41 participants in an HRE simulation. Eye tracking accurately identifies fixations on individual circuit elements and highlights critical components. Based on two use cases, we demonstrate that eye tracking and Think Aloud can complement each other to improve data quality. Our methodological insights can inform future studies in HRE, a specific setting of human-computer interaction, and in other problem-solving settings involving misleading or missing information.