The wastegate controls the boost that the turbo can create.
It's a fairly simple device. It's just a solenoid that swaps the input and output of the top pipe. This is the cycle valve.
The connector only has 2 connections. A positive connection and the negative connection.
The + and the - is actually printed on each side of the connector.
Without power, blowing through the top hose will make the air come out the hose on the right in the photo.
(electrical connector side). If you blow through the left hand tube, nothing will go through.
However, when you apply power, blowing through the top hose will make the air come out the hose on the left in the photo.
If you blow through the right hand tube, nothing will go through.
If the swap over doesn't happen or you can blow down the pipe that should be blocked off, it's broken.