The transmission solenoids are located under the side cover of the transmission. The side cover comes off with the transmission still in the car, but it's quite a job, especially if you don't have a lift.
Injuries or conditions that affect the chest wall -- the rib cage and associated muscles -- are another common cause of pleuritic chest pain. Chest muscle strain due to strenuous exercise may cause pain experienced primarily with deep breathing. Vigorous activity can also lead to costochondritis, a condition involving inflammation of the connective tissues of the rib cage.
Pericarditis is one of the more common cardiovascular causes of chest pain when breathing in deeply or coughing. Most other cardiovascular causes are not significantly altered by deep breathing. If the pain arises suddenly, then conditions like thoracic aortic dissection and pulmonary embolism also need to be considered.