Control backlight through HDMI on BBB

Hello,
I am working with a BeagleBone Black and an Ampire display (AM-1024600DTZQW). I would like to manage brightness with PWM, through HDMI and DDC protocol. Unfortunately, after much research, I am still stuck.

The HDMI of the BeagleBone uses i2c0 to communicate with the nxp TDA19988 controller. If I perform i2cdetect, I get the following result.

https://lh6.googleusercontent.com/w0YNbwMJbtk1cZD8vXvegt43BI5ao35nV6mhbfp8osaFo-cwRmE1ny_zPQ-BOuXHr9YVMsbxkx0FRFKY_tRLWjDCviRmAuec4a6rytj_-lBoDJI7FubZS5k_zbi04QyqFO-FDy0s

So I am missing the DDC address at 0x37. Moreover, if I try ddccontrol, I get this:

https://lh6.googleusercontent.com/VXmzvquHMW3Q-J-iPXNf_rBd_o5KnhH6BM_LN9CVPbLn_T-efpVdK8hTvtL5-lHTJIN6NZyr0l5K3e46swZezpoYaySy7QbMjutnwx67VOdSC2ZDIh3dAggVZSp8_ovJDCTjyWS1

However, I am able to read the edid with parse-edid.

My Ampire screen has been implemented with a firmware that supports DDC protocol. And it works fine when I connect it on my Linux PC.

https://lh5.googleusercontent.com/-rS28INAODoNapVknMlJxhrEE1Zmts5MIqvzcsF_CCW2RqGvqarwyR-19bIcYJ3PpqTTtxxhLeHYhkB96pAsqg-DdVE87If1kyxdvW5bkcXQkkz6kjkkEFCNF1IakRr3a0Qmihfc|952.8239113092422x541.1355657577515

Also, I had no problem working with my BBB and another display (Digital Display without DDC).

I don’t really have any more clues on how to solve this issue. Does anyone have an idea?