I don't know if you can set the cache order for icons considering it could constantly be changing if new programs were added, but you can set the notification to "Always show all icon and notifications on the taskbar".
To set this to be the default, go to this registry key:
HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\Explorer
Add the DWORD value "EnableAutoTray", double-click it, and set the hexadecimal value to "0".
I tested this and it worked.
Interesting note: I first tried to add it to this key:
HKEY_USERS\.DEFAULT\Software\Microsoft\Windows\CurrentVersion\Explorer
I have always thought that was the default registry for new users, but it did not work. So I went looking and found this interesting article busting my long-held thoughts about that .DEFAULT key.
http://blogs.msdn.com/b/oldnewthing/archive/2007/03/02/1786493.aspx
Addition: The best I can tell is that the registry entries are here If you were going to try and set one icon the way you would if you opened up "Control Panel\All Control Panel Items\Notification Area Icons":
HKEY_CURRENT_USER\Software\Classes\Local Settings\Software\Microsoft\Windows\CurrentVersion\TrayNotify
If you look at them, they are not very understandable, so I am not sure how well you would do editing them.
I suggest that you consider making a new user and its profile, set the "Control Panel\All Control Panel Items\Notification Area Icons" for that one icon (at least) to "Show Icon and Notifications".
Then reboot to release the profile, and log in as administrator. Copy that profile to the "C:\Users\Default" profile. You can do that either manually using Explorer, or the way we used to do it in "Control Panel\All Control Panel Items\System" "Advanced System Settings>Advanced>User Profiles>Copy to". It will be grayed out, but you can use the Windows Enabler to get around that.