P1690 is from when your clocks died.
With the ignition off, you can set the multimeter to 20v range, put the black probe on the battery -.
Put the red into the purple wire's female pin on the tacho harness plug, you should get 12v. Also agitate your harness while doing this to see if the voltage changes.
Start at the tacho plug and work back to the speedo plug, the heat grips, the accessory clock and the 12v accessory socket plugs.
Finally the underside of fuse #3 both pins.
The method should tell you where along the harness the fault in the purple wire is.
E.g. if all is fine from fuse to heated grips, but the voltage isn't a steady 12.x when you're at the speedo, then you know the fault is between heated grips plug and the speedo plug.
You can open the harness then to physically find the break in the purple.