Temp Gauge not working

[torkum]

I have a 1986 170 HP I/O. Had a very small fire (the voltage regulator fried) which burned some of the surrounding wires. Made all the repairs, including installing a new alternator kit and only thing left is that the temp gauge is blank. From what I've read the brown wire goes to the temperature sending unit.

My question: Per the attached picture (port side of engine), do I just need to run wire from the brown wire shown and up to the sensor on the same side of the engine? I don't want to short anything out but need to know my temp. Thoughts anyone?