To answer your original question, yes, a malfuntioning EBCM can definitely set the SSS light on. I don't know what these pin point tests are, but if we rely on your mechanic, the next step is to change the EBCM. If you are at all handy, and have some basic tools, it is one of the easiest repairs you can do on your car. Remove a couple of things to get at the EBCM, undo the electrical connector, remove a few attaching screws, then reverse the process. The EBCM is on the "dry" side of the brake system, meaning there is no brake fluid in it, meaning no mess and you don't have to bleed the system when you are done. As I stated in an earlier post, the best place I know to buy a used (but good) EBCM is from Morad. Do a google for Morad Car Parts. Send them an email with your vehicle'* VIN and they will be able to determine what the correct replacement part is. If they don't have the part in stock, they will tell you the part number, and suggest one or two other places that might have it in stock.
If you are not comfortable doing the work yourself, I would buy the used EBCM and pay your mechanic to install it.
2001 Bonneville SSEi (retired at 365,000 Kms.)
2014 Jeep Grand Cherokee Overland (yes, I know its not a GM)