This article presents a study of how co-present individuals work out the nature of embodied engagement and disengagement displays by individuals with dementia in a Danish public care facility. Research has found that moderate to severe dementia may result, for example, in a lack of social engagement, apathy and problems in maintaining conversations. Research has, however, also found that co-present individuals indicate their right to unavailability for social interaction. This is accomplished through details of embodied and multimodal conduct such as (...) gaze behavior, which includes practices of glancing and gazing at co-present individuals or practices of gazing into space. These practices may coincide with indications of ‘lack of social engagement’ and ‘apathy’. This study falls within the framework of ethnomethodology and employs multimodal conversation analytic methods to show how co-present individuals monitor residents’ displays of engagement and disengagement, primarily gaze behavior and how they respond to them. The study is based on 20 hours of video-recordings. (shrink)