Hi Jarryd, firstly is it a powertorque engine or the earlier type, full crank engine? I'll assume its a powertorque as the black and red wires would suggest they are part of the diode/charging setup from what was once an electric start mower, if they are just terminate them and ignore them.
The vacuum tube from the governor diaphragm goes to the nipple on the flywheel cowl just under the carb and off to the right a little.
And as Nathan said, pop off the diaphragm cover and remove the diaphram to "click" the ball back into position. Once it's in the easiest way to keep it there while you reassemle the carb is to open the throttle all the way thus turnig the cam and keeping itin position.
