As long as you have 20 ohms at the other end of that wire at the gauge you can elemnate the sender as a problem
To test the other end of the brown wire youll have to disconnect it from the gauge and meter it.
Above someone suggested seeing if the reducer gave you 6 volts at the gauge
When you get your new reducer you can meter it before you hook it up
Is the black wire off the reducer a ground wire?
Ive seen this style before
...click...Ignore the connections in that pic. It was from a member who wanted to know if he hook his gauge backwards. It is in that pic
But you can see the reducer can be installed and be out the way
