Newer vehicles have an almost unlimited number of relays, so no good info on which one you have there. Warning lights, seat belts. light on, etc. are some I think of.
But for the issue, I can go somewhat with your thinking on the flasher relay sticking or not making contact and how it might act, so I might go with the idea that the switch may not be "bad" as we might think of it, not making contact. One point on that is that it DOES kill the turn signal, so something is making in the switch?
My move might be to try pulling the switch to make sure there are not two wires making contact on the back of the switch or, even worse, something along the wiring, shorting the process out as the switch is thrown. Not all shorts in wiring do blow fuses. Would be handy if they did but they don't always do it.
Afraid this one may take some pretty good wiring diagrams and I find those hard to get. Part of the vehicle, not the coach wiring.