I would check with B&S support. Maybe they will provide some tech info. If it’s a warranty repair issue, they could probably refer you to a dealer in your area. They do seem to have some basic support FAQ’s and other general info on their website, but don’t know how much help that will be.
For replacement parts, on some sites, if you see a replacement part description with BNS Power in front of it, that stands for Briggs & Stratton Power. These guys in the link below sell OEM parts for the B&S transfer Switches. This is a parts breakout for the B&S branded 071046 200A ATS. Looks like the circuit board alone is $422.38, which is about half the price of a complete new transfer switch assembly.
B&S 200A ATS Parts Breakout 
