Turn signal intermittent malfunction?

The description sounds like a bad multifunction switch 8L8Z13K359AA. Moving it is allowing the internal contacts to disconnect. Replacement isn't hard but it's sort of fussy when it comes to the steering column cover tabs. Being plastic, you need to be gentle with them. However, to replace it you remove the trim panel from below the steering column by pulling down on the top latches shown as 1 in the attached picture then remove the three screws (item 4) that hold the plastic trim to the steering column. With those out you use a thin pry tool to release the tabs that hold the two shells together. Remove the two shells. Now unplug the two electrical connectors on the switch and the 2 screws that hold the switch to the column. Reverse the process to install the new switch.

Let us know what you find. Please.

The thing is that the way the system works it shouldn't be the SJB with that symptom. But stranger things have happened. If the SJB got corrosion in the connector it could cause strange things.

Just be careful, the SJB has a computer in it. This is the warning in service data Prior to the replacement of the module, it is necessary to upload the module configuration information to a scan tool. This information must be downloaded into the new Smart Junction Box (SJB) after installation. For additional information, refer to Section 418-01 See: Information Bus > Programming and Relearning > Programmable Module Installation (PMI). In the event that As-Built data is required (SJB (Smart Junction Box) does not communicate), all Remote Keyless Entry (RKE) devices must be programmed to the new SJB (Smart Junction Box). A minimum of 2 RKE (Remote Keyless Entry) devices are necessary to complete the configuration and turn off the flashing interior lights. The Tire Pressure Monitoring System (TPMS) functionality is integral to the SJB (Smart Junction Box).

That said, removing it isn't that hard. Use a trim stick to pop the bezel around the shifter off, then remove the cover and the console finish panel. Now you unplug the connectors and remove the bolts holding the SJB. Then clean things up and test it.
If you have a scan tool (FORScan is good for Fords and not real expensive) then you can run a self test on it and see if it has a problem.

Thanks for the update. Let us know how it works out.

Well, you could do some testing right at the connector for the SJB and that would eliminate any wiring issue and narrow it down. For that you would go to the SJB connector and use a couple T pins (find them in the sewing isle) that you will push into the back of the two wires that control the signals. That would be the Brown w/white wire on pin 29 and the brown with blue wire at pin 42. All the unit sees is one or the other getting grounded to select either side. So, if you unplug the switch and use the two pins and the signals work like they are supposed to you have a wiring issue. Possibly a bad ground wire to the switch, you could try this as well, go to the multifunction switch and find the Black wire w/blue stripe, which is the ground. Take a pin and push it into the back of the connector and just run a jumper wire from it to a good ground and see if things work. Testing is a pain but being it wasn't the most likely item, a bit of testing to keep from buying the SJB may be a good thing.