I would try turning the DS light on with the remote, this is also the one the hitch light is connected to. The other ODS light is not able to be controlled by the remote. If it does not come on with the remote either then I would suspect there is no power to the lights.
The red light on a fuse that is burned out will only come on if that switch is on to that circuit. It will not indicate a burnt fuse unless the switch is on. Turn those light switches on then check the fuse lights.
I would think both lights might be on the same fuse.
When I was checking my remote module today to assist in another problem I found that even with no power to the module those lights could still be turned on with the switches in the unit, as well the awning could still be operated. Those things could not be operated remotely with no power to the module of course. I don't think there is any problem with the remote module, since only one of the security lights is operational from the remote.
I am thinking a fuse.