Studies find that older adults want control over how technologies are used in their care, but how it can be operationalized through design remains to be clarified. We present findings from a large survey (n=825) of a well-characterized U.S. online cohort that provides actionable evidence of the importance of designing for control over monitoring technologies. This uniquely large, age-diverse sample allows us to compare needs across age and other characteristics with insights about future users and current older adults (n=496 >64), including those concerned about their own memory loss (n=201). All five control options, which are not currently enabled, were very or extremely important to most people across age. Findings indicate that comfort with a range of care technologies is contingent on having privacy- and other control-enabling options. We discuss opportunities for design to meet these user needs that demand course correction through attentive, creative work.