Edit the "Exp Pedal 0" settings block in global settings. Make it have the same settings as your main expression pedal settings, but add a System / Tuner action to the Position Switch Actions at the bottom of the page. Also, check the Invert Position Switch checkbox.
In the external switch settings, add a this action: System / Exp Pedal #1 off:0 on:Global. This will select the expression pedal settings that allow the tuner to turn on when the switch is off, and will select the expression pedal settings that don't activate the tuner when the switch is on.
After you send these settings to the GT, go into settings mode on the GT itself, and go to Exp Pedals / Exp Pedal 1. Then, put the expression pedal in the position where you want the tuner to activate (when it goes below that position), and press Set Switch Position on the GT. Read the settings back into the editor and save them.