(1) Goals: The purpose of this study was to analyze the feasibility of using the information obtained from a one-channel electro-encephalography (EEG) signal to control a mouse pointer. We used a low-cost headset, with one dry sensor placed at the FP1 position, to steer a mouse pointer and make selections through a combination of the user’s attention level with the detection of voluntary blinks. There are two types of cursor movements: spinning and linear displacement. A sequence of blinks allows for switching between these movement types, while the attention level modulates the cursor’s speed. The influence of the attention level on performance was studied. Additionally, Fitts’ model and the evolution of the emotional states of participants, among other trajectory indicators, were analyzed. (2) Methods: Twenty participants distributed into two groups (Attention and No-Attention) performed three runs, on different days, in which 40 targets had to be reached and selected. Target positions and distances from the cursor’s initial position were chosen, providing eight different indices of difficulty (IDs). A self-assessment manikin (SAM) test and a final survey provided information about the system’s usability and the emotions of participants during the experiment. (3) Results: The performance was similar to some brain–computer interface (BCI) solutions found in the literature, with an averaged information transfer rate (ITR) of 7 bits/min. Concerning the cursor navigation, some trajectory indicators showed our proposed approach to be as good as common pointing devices, such as joysticks, trackballs, and so on. Only one of the 20 participants reported difficulty in managing the cursor and, according to the tests, most of them assessed the experience positively. Movement times and hit rates were significantly better for participants belonging to the attention group. (4) Conclusions: The proposed approach is a feasible low-cost solution to manage a mouse pointer.