A synonym for “dull look” could be “listless gaze”.
The term “listless” implies a lack of energy or enthusiasm. When combined with “gaze”, it suggests a look that is without spark or animation. For example, “Her listless gaze betrayed her boredom.” This description gives a sense of apathy and a lack of interest in one's surroundings.
Another option could be “lifeless stare”. “Lifeless” emphasizes a lack of vitality or animation. A “stare” is a fixed look. For instance, “He gave a lifeless stare, as if his mind were far away.” This synonym conveys a sense of emptiness and a lack of emotion in the look.
“flat expression” could also work. “Flat” suggests a lack of depth or intensity. An “expression” refers to the look on one's face. For example, “His face held a flat expression, devoid of any excitement.” This phrase emphasizes the absence of any vividness or emotion in the look.