Feel like I could write a small book on everything arm care related for pitchers, after all of my research over the years. My son has had on/off again struggles with mechanics/timing so he has had to work really hard to stay healthy. IMO...most important thing your son can do is focus on soft-tissue, mobility, strength, and dynamic stabilization of cuff muscles. I can send you some exercises that my son uses on a daily basis as a college frosh. It is. As for long toss and pens, long toss is ok day after start with no set distance or reps. It should all be based on how your son is feeling. As long as he is performing in-season long toss correctly, meaning low-impact athletic throws the day after a start, and limiting distance out to 90-150, he should be good to go. No need for pull-downs day after start. Should continue soft-tissue, mobility, and strength work every day of the week. Day 2, should be similar but maybe a little more distance/volume. Day 3 would be more of a normal long-toss day, working out to normal long-toss max distance, and using intent pull-down throws. Day 4 should be normal long-toss with a pen. The pen should be based on feel as well but typically looking for 25-40 pitches. Day 5 should be a little like day 1 with distance out based on feel and no pull-downs. Day 6 similar to Day 5. Day 7 pitch but still use long toss as warm-up. Obviously this is the ideal situation. In your son's case, he would just modify based on days between starts. He can add in touch/feel flatgrounds or pens based on how his arm is feeling. The key is for him to pay attention to his arm and modify his routine based on days between starts.
Again, to spare everyone from a ridiculously long post, I can send you some detailed info on soft-tissue work and arm care exercises.