Since the condition is not painful, unlikely to be Priapism. Most common cause could be psychological, since it is associated with arousal. However it would be good to get an contrast MRI study to see for any vascular etiology.
It is Persistent Arousal Disorder . It could be due to injury to Pudendal Nerve or may be Psychological.Does he have erection only with excitement or spontaneously as well ? Priapism can be without pain . It is called High Flow Priapism . It is found in Blood Dyscrasia, Megaloblastic anemia. Investigate by blood count, detailed history and duplex sonography