If I've already played a Supporter this turn and use Sylveon's "Wink Wink" attack, can I still use the effect of a Supporter I discard from my opponent's hand?
Yes. You are not playing a second supporter, but using its effect via an attack.
Source: Forbidden Light FAQ (2018-04-20), TPCi Rules Team (2018-05-03)

Relevant cards

Note: All applicable cards may not be listed below.
SM6_87