Your version of the W123 may be similar to the W126. Startek is having some issues at the moment so I was unable to look at the W123 diagrams.
The Blower Speed Controller controls all speeds for the blower, including Hi-Low-Auto. It is also on its own fuse. The Pushbutton Controller is mainly for switching.
The same is true for the Temperature Controller. The Pushbutton Controller sets the mode and supplies the rheostat for variation. Everything else is controlled by the Temperature Controller.
Maybe you will have better success at opening the W123 diagrams than I did.
http://www.peachparts.com/shopforum/general-information/248948-mercedes-service-manual-source-cd-dvd-paper.html