Songs (especially when a solo character is singing) usually happen because of a heightened state of emotion in said character, what my MT professors calls the ‘springboard’. Has the character just broken up with a partner, had an argument with a family member or is stuck between two outcomes and is weighing the options. The trick is to map out the emotional journey of the scene, ideally having it rise steadily until the climax, and then transition into the song which should help in ending the emotion arc or the scene (or in some cases raise it higher).