Background:

Several FZ1OA members have said that their cluster loses its mind when the battery is low or is starting to get marginal, or when they start their bike. Also, the multigage voltmeter never really shows the battery voltage - it always seemed lower, particularly when the headlamps are on bright. So Paul Duffy and I did some voltage measurements to determine what is happening. What we found was surprising:

The voltage drop from the battery positive to the cluster was about 0.5 volts - this included several fuses, the key switch and the common wiring which carries most of the operating current to the fusebox.
On the ground lead from the cluster to the battery, there was another 0.6 volt drop, which increased to 0.8v+ when the headlamps were on bright. Please keep in mind that this is without incandescent running/turn lamps and cluster illumination, which easily could increase the total drop to 1.5-2.0 volts. What this tells me is that the ground wire is undergaged for the current level.

Reference: power feeds to/from cluster diagram.
Well Yamaha is smart, why would they do this?
We've done something similar before in automotive applications. Incandescent light bulb life is very much affected by the voltage across the filament, and as voltage increases, the bulb life drops very quickly (nonlinearly). So, the headlamps, the front running, and turn signals all share a common ground lead to drop the voltage that the bulbs see. But why do this for the cluster? It also has a bunch of peanut lights for illumination and for the warning lights. These will burn out more quickly also when voltage gets above about 12.5 volts. Please remember that the battery voltage can get as high as 14 volts while under charge.

So a separate power and ground system for the electronics portion of the cluster and the multigage was designed which permits full battery voltage getting to the cluster. The lighting circuit in the cluster will continue to retain some of the voltage drop by retaining its power feed. Best to replace the warning lights with LED’s when a bulb finally goes - see here.

Parts Required:

Two terminal connector.
Red and Black 16 gage wire or cable, 5 feet of each.
SPDT micro relay (.3x.4x.6 inch).
Tie straps, heatshrink and tape.
Inline fuse with holder—10 amp or 5 amp.
Ring terminal.

Action:

Remove seat and disconnect battery.
Feed one side of inline fuse through rubber boot and solder a ring terminal to this lead. Splice a 16 gage red wire to the other side of fuse. Bolt ring terminal to starter solenoid. Place heatshrink on inline splice.
After feeding through boot, solder black wire to battery terminal and route wire along battery cable, tie-strapping every 4 to 6 inches.
Remove LH side triangle panel, lift tank and support, remove LH side inner cowl panel, and remove windshield.
Route black and red wire along main harness, securing every 4 to 6 inches with a tie strap. At the front of the tank area route wiring through the wire tubing that runs to the left inner cowling area (by the voltage regulator). You will probably have to disconnect the existing connectors located under the LH side inner cowling to route the new wiring.
Install a connector next to the existing two connectors to facilitate future disconnection (or defer and install the connector in the future when you have to cut the wires.)
Continue to secure the red and black wires along the headlamp wiring harness. This can be achieved by threading under the front cowling or by removing the front cowling.
Cut the brown and black wires leading to the cluster, making sure that the cut is low enough to be able to retract the cluster connector boot. Splice the newly installed black wire from the battery directly to the cut black wire to the cluster. Solder and apply heatshrink.
Connect the relay as shown in the diagram and picture below. As you can see, the brown and black wires from the harness side are used to power the relay; the relay switches the newly installed "hot at all times" red wire to the brown wire heading to the cluster. Solder all connections and apply heat shrink to inline splices.
Secure the relay to the harness with tape. The relay is a sealed relay so no special precautions required.
Reconnect battery and reassemble trim parts. Go for a ride!

Addendum:

Comment from Schlumpf, the creator of the Multigage: Just one remark to add. You know that fuel-accuracy is one of the weak points not only of the multi-gage. The fuel sender/sensor is also supplied by the cluster! Most likely the accuracy should be increased noticeably. Currently the undetermined voltage shift leads to varying signals up to several liters. I just am not sure where he gets his ground from. Perhaps it is also easy to combine with your mod (if necessary at all)?

Response: I've done the voltage measurements on a full tank. The fuel sender ground is about 0.2 volts above ground with brights on and engine off, and the "signal" from the sender is only 0.5 volt--a very significant error.

It would be very easy to cut the ground lead from the sender connector where it enters the harness and jumper it to the new ground which passes right by there—see below:

The fuel level now did not shift when I turned the headlamp on and off. Success!!!