Dang! You caught me! I've been deliberately avoiding this topic because, the simple answer is "I don't know" mixed with "I forget".
Until just recently, I had Audition 1.5 (which is from about 10 years ago) installed on an old laptop but the DC input on the laptop has finally given up the ghost so I can't check anything.
So, working from memory, I think Audition 1.5 is one of the last versions before they implemented the ability to use ASIO drivers. If I'm correct, you'll need to prowl the Tascam download site to see if they have some US 1800 drivers that allow multitrack use with WDM/MME drivers. I don't think the generic Windows drivers allow more than two tracks at a time.
Again, from memory, the Audition menu you need is under Options/Device Properties. If you DO have all the tracks available, they should should up on a drop down menu there. Then, when setting up a session, there's a button in the box to the left of each track (by default it'll say Rec 1) that lets you select which track from the interface you want to go to each Audition track. I've not used the US 1800 but I'd bet there's also a Tascam menu for routing and mixing the various channels.
Anyhow, it might be worth asking the driver question of Tascam support.
If they don't do a WDM/MME driver for the US 1800, I'm not sure what to suggest. An upgrade to Audition 3.0 (which isn't sold anymore but you can sometimes see second hand) would do it as would a change to the current Audition CS6.
Apologies in advance if my memories are faulty--I blame age!