For purposes of a diagnosis please see the attached and refer to the following:
The OD Lamp in the Instrument Cluster (What Honda calls the "Combination Meter") is driven by what is called by various (although similar) names depending on what document you are looking at: "GP Sensor", "Gear Position Sensor", "Gear Position Switch" or "Switch Assembly, Change". FWIW, the Part Number for this item is: 35759-MCA-003 (Apparently no one at HMC talks to each other when it comes to document processing.)
Normal Operation:
There is a Green Wire with an Orange Tracer (G/O) that, among other things connects the GP Sensor with the instrument Cluster and the Cruise/Reverse Module.
If/when the GP Sensor grounds the Green Wire with the Orange Tracer (G/O) the Instrument Cluster should turn the Overdrive light "On".
Testing:
Start by locating the Green Wire with the Orange Tracer (G/O). The two easiest places to access this wire are: 1.) The 22 Pin Gray Connector (22P-Gr) that is located on the Left Side of the Fairing with the Top Shelter removed and 2.) The back side of the Instrument Cluster in Connector "A".
Note: Do not disconnect any wiring during any of these tests. If you must disconnect the Ignition Switch to remove plastic covers to gain access to any of these areas; be sure to plug it back in electrically for the duration of these tests.
With the Ignition Key "On" use a Jumper Wire to Ground the Green Wire with the Orange Tracer (G/O) at the Instrument Cluster. If the OD Light comes "On" the Instrument Cluster is good. If not, it's bad.
If the OD Light came on when you used the Jumper Wire to Ground the Green Wire with the Orange Tracer (G/O) at the Instrument Cluster, the failure is either in the wiring or the GP Sensor itself.
Next, if the OD Light came on when you Grounded the Green Wire with the Orange Tracer (G/O) at the Instrument Cluster. You'll need to check the wiring between the Instruemtn Cluster and the GP Sensor next:
Now ground the Green Wire with the Orange Tracer (G/O) at the 22 Pin Gray Connector (22P-Gr) that is located on the Left Side of the Fairing with the Top Shelter removed. If the OD Light comes "On" that will confirm that the wiring between this connector and the Instrument Cluster is good. If not, the Green Wire with the Orange Tracer (G/O) between this connector and the Instrument Cluster has an "Open" in it that will need to be repaired.
Next, if the OD Light came on when you Grounded the Green Wire with the Orange Tracer (G/O) at the 22 Pin Gray Connector (22P-Gr) that is located on the Left Side of the Fairing with the Top Shelter removed. You'll need to check the wiring between this connector and the GP Sensor:
Locate and ground the the Green Wire with the Orange Tracer (G/O) in the 6 Pin Black Connector (6P-Bl) that is located at the Top Front of the Engine with the Air Cleaner Assembly Removed. If grounding the Green Wire with the Orange Tracer (G/O) in the 6 Pin Black Connector (6P-Bl) that is located at the Top Front of the Engine with the Air Cleaner Assembly Removed does NOt turn the OD Light "On" there is an "Open" between this 6 Pin Black Connector (6P-Bl) and the 22 Pin Gray Connector (22P-Gr) that will need to be repaired. On the other hand, if the OD Light does come "On" that will confirm that all of the wiring between the GP Sensor and the Instrument Cluster is good. You will need to replace the GP Sensor.
Don't skip any steps and life will be much easier in the long run.