Sounds like you have a gauge cluster from a big truck such as a c60.
You mention "tandem and overdrive" as being used for signal indicators or wired to "the two orange lights" also you mention one green indicator for signal lights.
To the best of my knowledge this is more the big bolt configuration.
But that is neither here nor there as far as cancelling is concerned. If you have guts behind the steering wheel the fixes have been noted in other replies and I agree that more than likely you will find a malfunctioning cancelling cam.
If the guts of your system are located in a housing that appears to be part of the signal lever, normally attached to the steering column with a band,take it apart and check the springs,clean and oil all parts and reassemble.
The single green light indicator functions through a different configuration of the wiring harness and uses the same signal stat in the fuse panel.
Hope this helps,Hobert
