Distinguish Lutron Pico remote from paired switch

Hi all, we currently have a Lutron Caseta switch (PD-6ANS) that’s paired with a Pico remote, and we’re hoping to create an automation whereby turning off the switch triggers another switch to turn off too, but clicking on the Pico does not. We haven’t been able to achieve such with Google Home or Homekit, since neither can distinguish the switch from the remote; they can only respond to the light itself going off.

With Home Assistant, though, I gather the Pico would show up separately as a device trigger, https://www.home-assistant.io/integrations/lutron_caseta/. Given that, should we be able to distinguish whether a user has turned off the actual switch versus the Pico, in order to respond with an automation only to the switch?

Many thanks!