It's hard to say for sure, because there aren't a lot of places that prevent you from splitting aces, so there isn't a lot of strategy available that I could find about a soft 12 that says anything other than "split them, duh." From what I could find, it looks to me like the consensus is to play a soft 12 just a bit more conservatively than a soft 13.
One site I found recommends playing a soft 12 as a soft 13 unless the dealer has a 5 or 6 showing; in that case, he mentions doubling down on 13 through 18, but does not mention 12. That could be an oversight, or it could mean he would just hit a soft 12 ... he does mention a soft 12 in other situations. (I have seen this mentioned other places too ... not sure who posted it first.)
Another one plays them the same except for a 6, where you would double down with 13 but not with 12. That site specifically mentions a soft 12 separately from A-A (so you know to split aces if you can and hit if you can't - he does not recommend doubling down with soft 12 against anything.