Latest Brother Control Center and Catalina - Brother not supporting Apple OS
Maybe you saw this original post form March on this topic where the "helpful" response was one pointing you to the Brother site that suggested you search for the the Mac driver - all that gets you is the stone age v2 Mac Control Center - 1 32-bit incompatible application
So if you are unlucky enough to own a Brother Printer you are faced with a very poor choice
Don't upgrade to Mojave
OR
Find your Brother Printer/scanner functionality reduced
It seems pretty clear to me that the Brother strategy is to ignore Apple development and support and focus on Windows. The control center is now in v4 for windows but remained at v2 for Mac for the past several years. V2 control center is a 32-bit application and we have been receiving warnings from Apple for an extended period of time
Brother appears to have chosen to ignore them and has little interest in updating its drivers and software for their printers for Apple Cataline OS an 64-bit.
Their response has remained the same for a long time - you can find it here. Try this "new" application in the apple store "iPrint&Scan". But if you are like me you will find the list of compatible printers short and neither of mine featured
Or use the Apple Image Capture Utility - in other words we can't be bothered to support and write software for Mac users use the built in clunky tool that comes with Apple OS
I welcome being proved wrong but that's my exploration and at this point my relationship with Brother is now limited to the duration these printers survive and the consumables are used up at which point they will be retired and replaced with another brand that is interested in supporting apple OS for their printers