I am also having similar issues with the green arrows in the cluster and the turn/emergency signals burning solid rather than blinking.
This is all for Pre-FL R170...
The bulbs for the anti-theft alarm are different from the bulbs for the turn/emergency signals. I'm not 100% sure a failure of the PSE in the trunk can cause the "on but not blinking" scenario we both face (although the PSE often causes problems with other bulbs/filaments).
There are only three components that can blink the turn signal bulbs/filaments: 1) the turn signal switch on the steering column, 2) the red triangle, and 3) the lock confirmation relay. #1
receive a "blinking signal" from the CCM (in the apparatus box under the hood) and simply pass that on; #3
is controlled by the DAS module (not the PSE) and generates it's own blinking signal.
I've tried repairing the relay inside the CCM - this helped only for a few days. I've considered replacing the CCM and wiring an aftermarket flasher relay into the circuit. I've done neither yet.
I've also wondered if one of the above might be drawing too much current and causing the relay in the CCM to burn... replacing the CCM wouldn't fix that.