I examined the manual for your mobo and see that it does not clearly address the setup of the eSATA1 ports. That's like my mobo - few instructions, but it is hidden in there anyway.
On page 2-17 it starts Section 2-5 about the Integrated Peripherals. The third choice down is Onboard PCI DEvice, covered on page 2-19, and it includes the setup of the JMB363 Storage Controller involved here. From what little it says, within that menu you can enable or disable this controller which handles both IDE1 and eSATA1 functions, and you can configure the eSATA Controller Mode. Does not say anything more. BUT I suspect that, if you go into that, you will have an option for the eSATA1 controller to use or not use RAID. In fact, the "not use RAID" option is what you want, as you thought, and it could be labelled something else like "SATA" or "IDE" or some such. It might be as simple, though not obvious, as NOT checking a box to use RAID. Then as long as the eSATA controller is enabled but not set to RAID, it should work.
You will have to specifically Save and Reboot as you exit the BIOS Setup. Plug in your external drive on the eSATA port, make sure it is turned on, and reboot. Windows should find a new device and load its drivers. Then you can look for it in Disk Management. If your MyBook came partitioned and formatted already, you should be able to see it as a drive in My Computer. If not, you can use Disk Manager to do those tasks. In Disk Manager's right-hand panel at the bottom, right-click on the new unassigned drive and choose to Partition it. Split it up if you like, or make it one large volume using all the disk space. (Your OS must have support for "48-bit LBA" to make any volume greater than 127 GB.) Once the drive is partitioned, you right-click again on the partition(s) and choose to Format it (or them (one at a time), if you made more than one partition).
It's also possible that your MyBook came with a software CD with tools to do partitioning and formatting outside of Windows' Disk Management tools - I don't know because I have a different eSATA external drive. Either way, once the BIOS has been set to use the eSATA device WITHOUT RAID and Windows has loaded any necessary drivers, you must Partition and Format before Windows can see the device in My Computer and use it.