The information that you're trying to locate would typically have been kept on a Soldier's Field Medical Card (Medical Dept. Form No. 52c). Unlike the Emergency Medical Tag, this was not a duplicate document, and only the original existed. I have not seen any of these having been copied in official unit histories, and the only ones which I have seen completed have been in Veterans' collections.
If you have the soldier's ASN and full name, it might be advisable for you to try and use the NARA website to research his service, which might give some idea of where he served between the dates that you already know. The following link might be of use to you:
http://www.archives.gov/st-louis/milita ... ublic.html
Unfortunately, since the 1973 fire, it has often proved difficult for me to obtain any detailed information about a Vet's service without close contact with them, or their family. I wonder whether it would be possible for you to perform some genealogy research to highlight any relatives ?
Thanks, and good luck!