Your new tail light assembly - is it Honda OEM, or aftermarket? If it's aftermarket, and even though the connector is the same, it's possible that it doesn't contain a contact for "running light mode". Also, OEM or not, maybe the connector's bugged up somehow or there's a bad crimp on the individual pin for the running light.
Charlie you're on to it. It DID work. My riding pal said as he turned off last night, it was back ON for a minute.
So likely it's a loose connection.
The cool thing is it's not too much work to hook up, so worst case I go back to the OEM assembly, of which I have 2. the lenses might even fit, they're just clear.