You can try a couple of things. First see if they are remapping the Select button to the touchpad. In their converter manager program they show this table:
The other thing to try is to put the Quadstick into USB mode 7 and see if the touchpad passed through without remapping. USB mode 7 causes the Quadstick to say it is a Sony brand controller which might make the difference.
When I first tested the FGC2 I used Astro's playroom and it passed through motion and touchpad but I just saw this in an AI response:
The Brook Wingman FGC2 allows the use of a PlayStation 4 DualShock 4 controller on the PlayStation 5, including functionality for the touchpad in PS5-native games. However, the touchpad pressure function may not work by default when using the DS4 with the FGC2 on PS5 games, even though the controller is recognized.
To enable full touchpad functionality, users must configure the FGC2 using the Brook Converter Center software on a PC.
This involves creating a custom profile where the touchpad is enabled, specifically by setting the touchpad mode to "Mode 1" in the advanced settings.
After configuring the profile and synchronizing it with the FGC2, the controller should properly register touchpad inputs on PS5 games.
It is also recommended to set the PS5's controller communication method to "USB cable" in the system settings to ensure compatibility.
Without this configuration, the touchpad may not respond as expected in PS5 games, despite working in PS4 games or in Astro's Playroom