After 2 years of waiting for the official solution, hope is lost.
Today I deleted everything in my machine and installed Windows 10. After that I installed the suspicious firmware upgrade from the Asus forum:

https://bugs.launchpad.net/ubuntu/+source/linux/+bug/1653456/+attachment/4955397/+files/WinIAP_Fix%20Touchpad.zip
1. Download the Zip from the Link below
2. extract the zip into a folder where you want
3. open the "WinIAP_X64.exe"
4. select "Load Bin File" and now select the File "SB463D-1407_Fv0x06.bin" in the the same folder that you extractet
5. after the .bin file is loaded in the programm klick "Update Rom" (do nothing before the Update Process is finished)
6. when the update is finished, close the programm and restart your computer

After that, once again I deleted everything in my machine and installed Solus Budgie.
'ELAN1203:00 04F3:3043' touchpad of my Asus G752VS laptop finally works perfectly on Linux.