Instruments such as eye-tracking devices have contributed to understanding how users interact with screen-based search engines. However, user-system interactions in audio-only channels -- as is the case for Spoken Conversational Search (SCS) -- are harder to characterize, given the lack of instruments to effectively and precisely capture interactions. Furthermore, in this era of information overload, cognitive bias can significantly impact how we seek and consume information -- especially in the context of controversial topics or multiple viewpoints. This paper draws upon insights from multiple disciplines (including information seeking, psychology, cognitive science, and wearable sensors) to provoke novel conversations in the community. To this end, we discuss future opportunities and propose a framework including multimodal instruments and methods for experimental designs and settings. We demonstrate preliminary results as an example. We also outline the challenges and offer suggestions for adopting this multimodal approach, including ethical considerations, to assist future researchers and practitioners in exploring cognitive biases in SCS.