Evaluating the mediastinal position in a client with chest trauma is best done by palpating for tracheal deviation. Mediastinal shift, often caused by conditions such as tension pneumothorax or a large hemothorax, can lead to tracheal deviation. While auscultating breath sounds, palpating for crepitus, or auscultating heart sounds provide valuable information about the patient's respiratory and cardiac status, they do not directly indicate the mediastinal position. Tracheal deviation is a direct and reliable sign that can indicate a mediastinal shift.