An assistive technology developed for "hands free" control of electrical devices to be used by severely impaired people within their environment, relies upon using signal processing techniques for analyzing eyes closed (EC) and eyes open (EO) states in the electroencephalography (EEG) signal. Here, we apply a signal processing technique used in continuous chaotic modeling to investigate differences in the EEG time series between EC and EO states. This method is used to detect the degree of variability from a second-order difference plot, and quantifying this using a central tendency measures. The study used EEG time series of EO and EC states from 33 able-bodied and 17 spinal cord injured participants. The results found an increased EEG variability in brain activity during EC compared to EO. This increased EEG variability occurred in the O2 electrode, which overlays the primary visual cortex V1, and could be a result of the replacement of the coherent information obtained during EO by noise. A continuous measure of the variability was then used to demonstrate that this technique has the potential to be used as a switching mechanism for assistive technologies.