I still think using a cable is better no matter in what mode you use your camera. I repeat Ihave not used the TG-6 ( I will have it by the end of next month in a Seagfrogs hosuing).
I imagine the the light of built-in flash passing thru the plastic of housing might be weak and might not trigger the external (at least that happens with the housing I have owned (not many: Fantasea fon Canon G7X and Seafrogs for Sony 6300).
There are afordable options for fiber optic cable. You can by it by lenght with the connectors needed for your housing and strobe in www.divervsion.com.
The built-in flash is enough to trigger the external strobe, but the timing is off. That's what confused me for so long since my strobe is firing and everything seems fine. Then online resources such as Backscatter, INON, or other websites all state that you don't HAVE to have a cable, just turn flash to fill-in, and set the strobe to STTL.