Alzheimer’s disease (AD) dementia is associated with marked disruptions in resting-state eyes-closed electroencephalographic (rsEEG) rhythms, particularly in the periodic alpha band (8–12 Hz), suggesting impaired vigilance regulation. In contrast, the aperiodic rsEEG component, reflecting global cortical arousal, has been reported to remain unchanged. This exploratory study examined periodic and aperiodic EEG activity in patients with mild cognitive impairment due to AD (ADMCI) during transitions from quiet wakefulness to light sleep. EEG datasets (∼30 min) from 19 ADMCI patients and 18 matched cognitively unimpaired older adults (control) were analyzed. Vigilance stages were scored using a reduced version of Hori’s system, distinguishing the alpha-dominant wakefulness stage and the theta-dominant light sleep (ripples) stage. EEG spectra were parameterized using the specparam algorithm. ADMCI participants showed reduced reactivity of individual alpha power between the wakefulness and ripples stages compared to the control group. Conversely, both groups exhibited comparable increases in fronto-central theta power and steepening of the aperiodic slope and offset. No group differences emerged in aperiodic exponent and offset, although statistical power was limited by modest sample size. Overall, EEG alpha rhythms reflecting vigilance regulation are disrupted in prodromal AD, while periodic and aperiodic signatures of sleep onset are relatively preserved, suggesting selective vulnerability of attentional thalamocortical systems.