I've taken it from 0.5mg to 1.7mg every other day to "improve immunity" for repeating headaches, constantly irritated throat, and "sensitivity to cold weather". I measured one time it increased Lymphocytes but not Neutrophils, although the Lymphocyte increase could be immune activation from infection not from thymosin itself. It did not stop the recurring headaches, reduced the irritated throats and possibly increased allergic immune reactions with shortness of breath.
If your immunity is fine but you want to "optimize it", my advice is to not take it. It is not studied well, nobody knows what exactly it does, and it may bring you new problems if it stimulates the immune system the wrong way.
If you want better immunity, take probiotics and eat probiotic foods. 70% of your immune system is around the gut and is modulated by the microbiome there, so make sure you have lots of the "good bacteria", which displace the bad ones and that by itself will improve your immunity. This has a more profound effect on immunity than most people believe.