A short story I think... A man who suffers from blackouts hires a husband and wife detective team to follow him when he's in his fugue state... I thought it was a Philip K Dick short but couldn't find it online. Possibly by Douglas Adams... Ring any bells?
"The Unpleasant Profession of Jonathan Hoag", a fantasy novella by Robert A. Heinlein, also the answer to this old question and this one, and an unaccepted answer to this one; first published in Unknown Worlds, October 1942, available at the Internet Archive.
From the Wikipedia plot summary (emphasis added):
A man comes to an investigator with an odd request: he wants to have himself followed, because he has no idea what his own profession is. The story evolves into a discussion of the reality of both life and art.
Jonathan Hoag, a lover of art and fine dining living in Chicago, realizes that he has no memory of his daytime activities when asked, at an evening dinner, what he does for a living. Furthermore, when he washes his hands in the evening, he discovers a red-brown substance, possibly dried blood, under his fingernails.
He contacts a detective agency, Randall & Craig, and asks them to follow him during the day. The partners, actually the husband and wife team of Ted and Cynthia Randall, agree to this. The mystery begins immediately: they try to collect fingerprints from their client, but find that Hoag left none, even when not wearing gloves. The few memories Hoag has turn out to be false, except for his home address, and a doctor, Potiphar T. Potbury, whom Hoag consulted about the substance under his fingernails. The doctor had thrown him out of his office and told him not to return.
[. . . .]
To solve the mystery once and for all, they take Hoag to their office and subject him to questioning under drugs. After a few questions, Hoag wakes up with a strong, dominant personality—completely different from the nervous, weak man they have heretofore worked with. He declares the session over, and tells them to meet him later in a park just outside the city. He gives them a list of things to bring, and leaves them in a state of some puzzlement.
Reaching the park, with the collection of fine foods and wines Hoag requested, Ted and Cynthia find him there. They picnic on the epicurean fare, and Hoag tells them he is an art critic. The art in question is their entire world, created by an "artist" as a student project. Critics live as inhabitants in the world, not knowing they are Critics, in order to judge the experiences. One such experience is eating and drinking, as Hoag points out, since the simple act of gaining energy to live had not been thought of as an "experience" previously. Another is sex, but this is thought to be ridiculous until Hoag realizes that it is the basis for "the tragedy of human love" that he sees between Ted and Cynthia. Hoag's artistic judgment is that, while there is much that is amateurish in the world, overall its Creator has real promise.
The Sons of the Bird are responsible for all the things that Ted and Cynthia have seen, including the times they saw Hoag during the day. They only encountered the real Hoag in their home and office. The Sons were an early artistic mistake, hurriedly "painted over" rather than eliminated in the rush to complete the work, but still holding power. Now they are to be expunged completely. Hoag was recruited to report on them; the substance under his fingernails is their ichor, placed there to make them fearful.
Hoag tells the couple to leave the city, not stopping to talk to anyone on the way. He places one last grape in his mouth, and then becomes still. Leaving his inert body, the two drive through town, but finally yield to the urge to tell someone about Hoag's body. When they roll down their car windows, however, all that is outside their automobile is a pulsing, luminous mist, though all the other windows show an apparently normal scene. They drive on in a state of shock.
Not a short story, but this fits: "The Bad Place" (1990) by Dean Koontz - a sort of sci-fi horror cum mystery.
Frank Pollard wakes up in an alley at night, filled with confusion and fear. He knows nothing but his name, and that he must escape fast, or else he will be killed. Pursued by a mysterious assailant, Frank barely escapes with his life.
Every time he goes to sleep, he wakes up to find evidence of bizarre nighttime travels which he cannot remember. Afraid of his own actions, Frank enlists the help of husband-wife security team, Bobby and Julie Dakota.
Although the entry says security team, they are closer to private detectives.