Thrawn was born in 59bby. He meets Eli & joins the Empire in 14bby, making him about 45-46 years old to Eli's estimated 20-22 (he's in his 3rd year of academy on Myomar.)
Note: I am guesstimating Wild Space recruits to join up between ages 17-20, maybe a little later because of core world prejudice leading to their lack of faith in Wild Space education systems, etc, but this is based on the way Eli is treated rather than any basis in fact.
I mean... I know he's not exactly who most people imagine Eli as, but imo he'd be perfect for him. He's Australian, so he'd have a different sort of "twang", but let's be honest Australia is basically just the Commonwealth's equivalent of the American South.