As it turned out (thanks to the bus_monitor.py from https://gitlab.com/py_ren/pyren/ project which makes ELM327 to be the simpliest can bus hacker tool) the display wanted to be awaken by a pair of can frames being sent on the can-v (can vehicle) wires.

To figure that out I simply recorded a pair of traces taken from both can buses on a real car and then tried playing them back frame-by-frame to my radio and display guinea pigs. The beast awoke and started roaring :)

struct can_frame external_temp = {
  0x534, 0x5, 0x80, 0x00, 0x00, 0x00, 0x2C, 0x00, 0x00, 0x00
};

struct can_frame wakeup_radio = {
  0x35C, 0x8, 0xf1, 0x06, 0x56, 0x11, 0x18, 0x3e, 0x62, 0x14
};

struct can_frame wakeup_display = {
  0x35C, 0x8, 0xf1, 0x06, 0x56, 0x11, 0x18, 0x3f, 0x62, 0x14
};