I also cannot find any records of any other active T-38 with xx194, although some xx194 had been passed on to the US Navy and receiving different serials.
https://www.joebaugher.com/usaf_serials/1964.html
So perhaps a painters mistake? It wouldn't be the first. As per the late Joe Baugher, 64-13194 (the 3 mistakenly used as FY?) returned to the 71st FTW in 2003. However Scramble has a later record of it in March 2022 confirming the RA code and 435th FS. By then it was in the standard 2 tone grey scheme. So very likely this is your bird and after the new blue coat they applied the serial incorrectly.
Still not 100% unless you read the datablock.