Server 2012 Core.
I can manually check for Windows Updates with sconfig option 6. I can set Windows Updates to automatic with sconfig option 5. Great.
What if I want to change that to 4 AM? What if I want to change it to only check once a week?
I sniffed around in HKLM:\Software\Microsoft\Windows\CurrentVersion\WindowsUpdate\
but didn't see anything that looked like it let me fine tune the schedule like I want.
Assuming this isn't a domain machine you can configure through domain Group Policy, you should be able to connect a local Group Policy Editor mmc to the core machine from a full client and set the local policy that way (assuming 2012 still works as 2008 did):
http://blogs.msdn.com/b/neilhut/archive/2007/11/06/managing-local-policy-on-a-windows-server-core-installation-set-to-workgroup-config.aspx