Take a look at the chart below. It's for the 2013 RT but I think it's basically the same for the 2011 RT. To me, what you are describing doesn't jibe with the switch functions. All the switch functions in that chart are for circuits that feed into the processor board in the MSL. Let's call the turn signal connections R, L, and Gnd. As you can see when you press the switch in both R to Gnd and L to Gnd connections are made. As I see it the only way the switch would cause the left signal to come on as you describe it, the R to Gnd connection isn't being made when you press the switch in for cancel and the L to Gnd is being made. When you push the switch to the right you make a R to Gnd connection. When you push it left you don't make a L to Gnd connection. But why would pushing the button in not make the R to Gnd connection when pushing it to the right does? And why does pushing the button in make the L to Gnd connection but pushing it to the left does not?
Keep in mind the turn signal switch is not connected to the turn signal lamp circuits. It is connected only to the MSL processor board. The processor sends a digital signal over the CAN BUS to the cluster. The cluster then operates the left and right turn signal circuits. Either the MSL processor is not sending the correct signal to the cluster, or the cluster board is messed up. Now, if the MSL sent a goofy signal to the cluster maybe that caused the cluster to flash the left signal rapidly. I'm inclined to think one of three things is happening. First, the switch has failed in a really weird way causing the MSL processor to get some really goofy signals thus causing it to send out no or bad CAN BUS signals, or second, the MSL processor is failing and simply sending wrong or no signals to the cluster, or three, the cluster is failing. Since two of the three possibilities are the MSL, and it's cheaper to replace than the cluster, let's hope it's the MSL. But the symptoms tend to make me think it's the cluster. The Spyder clusters have had very few problems so that would point against it being a cluster problem.
Do this for a test. Press in the Mode, Set, and Turn signal buttons simultaneously with the engine running. Do you get a blank screen or any codes showing? If the procedure for checking fault codes fails then for sure you've got a bad MSL. If the code screen comes up correctly that is an indication, to me anyway, that the MSL is working. If that's the case I suggest you go to your dealer and have them connect it to BUDS. I don't know what all can actually be read with BUDS but there is an option to read data, and the cluster is one of the units it will read data from. I'm guessing there is a whole separate manual for BUDS with a lot more info than the regular service manual has. If no codes show, but the screen looks correct, there is one sure way to generate a code. Raise the rear tire off the ground, put it in gear and run it up to 20 or 30 mph for a several seconds. You'll get a code because the front tires aren't turning. Then check to see if the 3 button push brings it up. Be sure to do that before turning the ignition off.
If you end up buying an MSL I'd look first online to a motorcycle salvage yard. That's one of the items that most likely won't be clobbered in most wrecks so you should be able to find a good used one. Good luck chasing this down.