The PC should be effectively Columbo in any murder-mystery
. They have an inherent feel for who did it, but still need to get the bad guy to reveal their hand, so they can deal with them in front of witnesses.
Introduce complications for bare-faced accusations against high-ranking NPCs. These heroes are relative nobodies, what exactly are they doing accusing the nobility, when everyone knows they should be not wasting important peoples time, and be checking the bandits in the swamp for clues . . .
Like any murder mystery, have plenty of misguided and dodgy characters around who seem suspicious, but aren't necessarily evil or connected with the main plot. The classic "No I wasn't there, but I can't give an alibi (because actually I was there, but was poaching from the king, plus I heard something but daren't say)". These people should trigger that something is up on a sense motive.
Don't ping true/false "lie" for high sense motive results when the ability is used directly. Most people expect a direct approach and will mentally prepare a good lie/alibi. Instead give out "he seems distracted", "you sense she is concealing something" or "the question shocks them" or "you've just made them really angry/sad".
Give out better sense motive results when the skill is used in conjunction with subtler approaches than direct questioning, such as following someone and watching what they do, who they talk to - who are their true friends amongst the courtiers, do they share a secret with the shop-keeper etc, etc.
In general, make it clear that the skill is useful, but it is only one part of a good detective's toolkit. The character, or other party members, need to apply other skills and approaches to fully out a criminal.

Introduce complications for bare-faced accusations against high-ranking NPCs. These heroes are relative nobodies, what exactly are they doing accusing the nobility, when everyone knows they should be not wasting important peoples time, and be checking the bandits in the swamp for clues . . .
Like any murder mystery, have plenty of misguided and dodgy characters around who seem suspicious, but aren't necessarily evil or connected with the main plot. The classic "No I wasn't there, but I can't give an alibi (because actually I was there, but was poaching from the king, plus I heard something but daren't say)". These people should trigger that something is up on a sense motive.
Don't ping true/false "lie" for high sense motive results when the ability is used directly. Most people expect a direct approach and will mentally prepare a good lie/alibi. Instead give out "he seems distracted", "you sense she is concealing something" or "the question shocks them" or "you've just made them really angry/sad".
Give out better sense motive results when the skill is used in conjunction with subtler approaches than direct questioning, such as following someone and watching what they do, who they talk to - who are their true friends amongst the courtiers, do they share a secret with the shop-keeper etc, etc.
In general, make it clear that the skill is useful, but it is only one part of a good detective's toolkit. The character, or other party members, need to apply other skills and approaches to fully out a criminal.