A sentence from the abstract of The population of natural Earth satellites states:
At any given time there should be at least one NES of 1-meter diameter orbiting the Earth. The average temporarily-captured orbiter (TCO; an object that makes at least one revolution around the Earth in a co-rotating coordinate system) completes (2.88 ± 0.82) rev around the Earth during a capture event that lasts (286± 18) d.
As far as I know, the only known, well documented temporarily captured Earth satellite is 2006 RH120, which was in within 1 million km of the Earth for about 1 year. It has an estimated size of 2 to 3 meters, a rotation period (about it's axis) of about 3 minutes (presumably determined by photometry). According to Wikipedia:
2006 RH120 was discovered on 14 September 2006 by the 27-inch (690 mm) Schmidt camera of the Catalina Sky Survey in Arizona.
Using data from the JPL Horizons database, it seems 2006 RH120 was only about 850,000 km from Earth at the time it was discovered.
Deep sky surveys are extremely prolific at detecting small solar system bodies. There was also a recent answer addressing the possibility that the Gaia spacecraft's could detect trojan asteroids associated with Earth's orbit, linking to the paper Detection of inner Solar System Trojan Asteroids by Gaia.
The question asked specifically about TCO's being detected by Gaia, but my question is more general: How would a small TCO (temporarily captured orbiter) or other natural Earth satellite most likely be detected?
There are Earth-based sky surveys, space based visible and near-visible, and possibly even infrared/thermal detections possible, even Earth-based radar, and possibly others.
Are there any searches specifically targeting TCOs?
above: a simple plot of the orbit of 2006 RH120 from JPL Horizions transformed to an Earth-centered Earth-Sun-synodic frame - red line with dots every 10 days, for the period when it was within a +/- 1.6 million km cube centered on Earth in this frame. The green thick band around Earth is the moons orbit during this 448 day period.