Or alternatively just have the passive ability be hindered when an action is performed. When in battle I wouldn't expect my trap detector to be functioning at full capacity as other things are on his/her mind, but there should at least be some chance that they will spot the tripwire or avoid the slightly different coloured floor tile. Just make it more difficult for them, and then fights which include traps will be easier for a party that includes a master of trap detection, whereas parties who just want to detect static traps outside of combat could get away with somebody with somewhat less skill.
This removes the "player activity" as you say and also seems more lifelike.