You're right, sorry! I included the debug nodes:
The wall switch indeed seems to send an empty string into the process. But I'm not sure if that's the issue here, since I can click it again right after clicking the first time, and it will send another message into the flow:
In the second image, you can see that I'm clicking the button 1 second later. The call:service node responds with light.toggle called at: April 12, 11:02 even though the physical light did not toggle. I can keep clicking the button, and after 20 seconds or so the light will eventually toggle.
I've included the export of the flow, should that be helpful:
[{"id":"fe972f0b.5e0eb","type":"tab","label":"Test","disabled":false,"info":""},{"id":"cbfd5733.975038","type":"server-state-changed","z":"fe972f0b.5e0eb","name":"Double key switch","server":"3ecfd5ab.de166a","version":1,"exposeToHomeAssistant":false,"haConfig":[{"property":"name","value":""},{"property":"icon","value":""}],"entityidfilter":"sensor.0x00158d0002b4a074_click","entityidfiltertype":"exact","outputinitially":false,"state_type":"str","haltifstate":"","halt_if_type":"str","halt_if_compare":"is","outputs":1,"output_only_on_state_change":true,"x":130,"y":140,"wires":[["6ef37698.e06ef8","58fe02da.179d5c"]]},{"id":"6ef37698.e06ef8","type":"switch","z":"fe972f0b.5e0eb","name":"","property":"payload","propertyType":"msg","rules":[{"t":"eq","v":"left","vt":"str"},{"t":"eq","v":"right","vt":"str"}],"checkall":"true","repair":false,"outputs":2,"x":230,"y":240,"wires":[["a6b14158.d555b","17cc9072.ac71a"],["dec4ee1b.58ba4"]]},{"id":"58fe02da.179d5c","type":"debug","z":"fe972f0b.5e0eb","name":"DK wall switch","active":true,"tosidebar":true,"console":false,"tostatus":false,"complete":"payload","targetType":"msg","x":370,"y":120,"wires":[]},{"id":"a6b14158.d555b","type":"api-call-service","z":"fe972f0b.5e0eb","name":"Light 1","server":"3ecfd5ab.de166a","version":1,"debugenabled":false,"service_domain":"light","service":"toggle","entityId":"light.shelly_shrgbw2_6ee67e","data":"","dataType":"json","mergecontext":"","output_location":"","output_location_type":"none","mustacheAltTags":false,"x":410,"y":200,"wires":[["3692a542.0ba66a"]]},{"id":"dec4ee1b.58ba4","type":"api-call-service","z":"fe972f0b.5e0eb","name":"Light 2","server":"3ecfd5ab.de166a","version":1,"debugenabled":false,"service_domain":"light","service":"toggle","entityId":"light.shelly_shrgbw2_6ee67e","data":"","dataType":"json","mergecontext":"","output_location":"","output_location_type":"none","mustacheAltTags":false,"x":408,"y":274,"wires":[[]]},{"id":"17cc9072.ac71a","type":"debug","z":"fe972f0b.5e0eb","name":"Switch","active":true,"tosidebar":true,"console":false,"tostatus":false,"complete":"payload","targetType":"msg","x":220,"y":400,"wires":[]},{"id":"3692a542.0ba66a","type":"debug","z":"fe972f0b.5e0eb","name":"Light 1","active":true,"tosidebar":true,"console":false,"tostatus":false,"complete":"payload","targetType":"msg","x":600,"y":200,"wires":[]},{"id":"3ecfd5ab.de166a","type":"server","z":"","name":"Home Assistant","legacy":false,"hassio":true,"rejectUnauthorizedCerts":true,"ha_boolean":"y|yes|true|on|home|open","connectionDelay":true,"cacheJson":true}]