With the parameters "Split Menu" and "Menu Count" together you are able to split a menu within a single module - this is what you don't want.

With the parameters "Begin With Level" and "Split Menu" you are able to split a module into separate modules... you will need to use the "Copy" toolbar button to duplicate the module... so that you for example set the 1st to the module position "top" and the other to "right".

Then for the 1st menu module set "Split Menu" (same meaning as "Maximum Depth" in that special case) to "1" (leave "Menu Count" at "1"). While on your 2nd menu module you need to set "Begin With Level" to "1".

When there are no menu items for the 2nd module to display the area will appear empty.

(Edit: Btw. instead of the 1st menu module you could use also the regular mainmenu or another menu module to display the first level)