If Empoleon V with "Emperor's Eyes" Ability is in the Active Spot and my opponent brings up a Klefki with "Mischievous Lock" into their Active Spot, whose abilities are turned off?
Since Emperor's Eyes was in effect before Klefki became active, it takes precedence and Mischievous Lock does not activate as long as Emperor's Eyes is in effect. The converse is also true, if Klefki were active first and Empoleon V is brought up, Emperor's Eyes would not activate.
Source: TPCi Rules Team (2023-04-06)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH5_40
SWSH5_40
SV1_96
SV1_96