Hi, I've just gone through this as well. I recommend taking the extra time to remove the right-side cover (it's only 5 screws) so that you can fully access the service area. Without doing this you can only see part of the service area, because the capping section is retracted inside. On mine, it was the capping station that had the most gunk requiring cleaning. With the right cover removed there is a Torx T10 socket on the back of the printer that you turn to advance/retract the capping station. This allows you to position it wherever you want to more fully clean it.
The service manual provides more detailed instructions on how to remove the right cover, and the location of the T10 "screw" socket.
After cleaning you can operate the printer for a few tests with the right cover off. You can see the service area and capping station in operation to better understand how it moves and how the gunk collects on it. You may need to clean it a bit more after operating a few times as more of the gunk appears from hidden areas.
Another side benefit is that you can see fully into the carriage area while it is printing, scanning cal/profile targets, etc, which is kinda neat to watch if you're into that sort of thing haha
Hope that helps!