Re: What do these three wires do?
The socket..... If you're spaeking of the hole in the back of the tach, my guess is that a light bulb goes in there. Exactly what kind of bulb socket.
I can't make out what the back of that tach looks like. A hint in picture taking is to have the area well lighted, and kill the flash feature on the camera. This will give a clearer picture (works for me anyhow).
But, at any rate, let us know what connections exist on the back of that tach, how many, what are they marked?
Should they be marked something like "G" or "GND" (ground), this would be the black wire connection.
A connection marked "S" or "SEN" (sensor), this would be the gray wire connection.
A connection marked "+", or "POS", or "BAT" or "12v" would be the purple wire connection.
If a dial exists on the back of the tach, try setting it on #6.
Let us know what you find.