This question is way above my pay grade, but then I am retired... I believe that a press of the Emergency Button via programming in the radio will send an Emergency Alarm Request from the Subscriber Unit (SU) on the uplink channel as an ISP message with an Opcode of 0x27.
Now I don't know for sure, and it likely varies somewhat by system manufacturer, but I believe that this would show up on the associated downlink channel (Trunk) as a Group Voice Channel Grant message with the Emergency Bit set in the Services Options octet of packet.
There is also a Motorola Proprietary OSP called "Motorola Emergency Alarm" that perhaps may be transmitted in response to an SU with an emergency activation on Motorola systems?
Hopefully, someone who fully understands P25 trunking protocols will offer a better or more accurate description of the messaging involved with this process. I'd actually like to know for certain myself. I can't tell you if programs like DSD+ or SDRTrunk are capable of flagging these events or not.