I'll look at the CAN log in detail later. It's interesting what you have achieved.
The 0x501 message was only about keeping the module awake. What it does when awake, whether the display comes on, and whether the numbers react to the knobs, was never going to be affected by the 0x501 messages. There would always be other messages for that.
On the one hand you got the module to stay awake with the 0x501 message, but on the other hand the log that you took from a real car didn't have the 0x5xx messages behaving in a way that would have worked to keep the modules awake and let them go to sleep. It seems likely that there is more than one way that the modules can be operated.
Similarly, the temperature signal from the module could be "up" and "down" and some other ECU decides the temperature for the module to display, or the output could be the temperature itself. Also, both schemes could be possible on one module, and what is used depends on what the rest of the car does. The HVAC module that I worked on a few years ago was a rear HVAC module, and I only ever saw it work in the first mode. When playing back a recorded CAN trace, the temperatures didn't respond to the knobs, but they did respond to the the CAN signals.
The 0x501 message was only about keeping the module awake. What it does when awake, whether the display comes on, and whether the numbers react to the knobs, was never going to be affected by the 0x501 messages. There would always be other messages for that.
On the one hand you got the module to stay awake with the 0x501 message, but on the other hand the log that you took from a real car didn't have the 0x5xx messages behaving in a way that would have worked to keep the modules awake and let them go to sleep. It seems likely that there is more than one way that the modules can be operated.
Similarly, the temperature signal from the module could be "up" and "down" and some other ECU decides the temperature for the module to display, or the output could be the temperature itself. Also, both schemes could be possible on one module, and what is used depends on what the rest of the car does. The HVAC module that I worked on a few years ago was a rear HVAC module, and I only ever saw it work in the first mode. When playing back a recorded CAN trace, the temperatures didn't respond to the knobs, but they did respond to the the CAN signals.