It's true that it's not stated anywhere. But, the way this is processed during the boarding is that passengers on Go Light are boarding in the last group. Staff doesn't stop carry-ons while previous groups board, only when boarding opens for Go Light. As *G gets priority boarding, it should be no problem to board with a carry-on, unless they arrive at the gate during the last phase of boarding. I would imagine that for this reason they might allow carry-ons (not printing "no carryon" message on BP) for *G, even if it's not officially stated.

OP: Try making a dummy booking. During the booking flow your baggage allowance will be shown (on the page where it offers you to buy extra bag), which does reflect status benefits if you provided FFP number during previous steps. As EBG I see 1 carry-on allowed, so if there's an exception for *G too, it should be shown as well.