Most players do one of two things after a tryout: nothing at all, or too much. Both cost opportunities.
The organizations you are contacting are small. A typical independent league front office might have a handful of full-time staff, and the person who ran your tryout may also be the manager, the pitching coach, and the person handling roster paperwork. They are not ignoring you out of disinterest — they are busy.
Understanding that shapes everything about how you follow up.
The Core Principle
Make yourself easy to say yes to, and easy to find later.
That is the entire objective. You are not going to argue your way onto a roster in an email. What you can do is stay on the radar, be professional, and make sure that when a roster spot opens in June, your name and your numbers are three clicks away.
Timing
Within 48 Hours: The Thank You
Short. Professional. No ask beyond staying in touch.
This email exists to attach your name to a face and put your contact information in their inbox. That is it.
Two to Three Weeks Later: The Update
Only if you have something genuinely new — a velocity increase, a strong performance somewhere, a new video. Not a check-in for the sake of checking in.
Monthly, at Most: The Light Touch
If you are still unsigned and still interested, a brief note once a month is reasonable. More than that becomes noise.