From the Super Mario Wiki
Speedy Spirits are rare ghosts found in Luigi's Mansion.
Speedy Spirits are pale blue and have a similar build to a Gold Ghost. Unlike others who attack Luigi, Speedy Spirits hide from him. If they are discovered by examining an object, they panic and try to run off. Luigi must shine his Flashlight on it and immediately suck it up before they flee. If Luigi manages to capture one of them, it yields a large amount of treasure, which always includes Coins, but sometimes includes valuable treasures, such as Stones. There are a total of fifteen Speedy Spirits in the Mansion. Gold Mice are similar treasure yielding Ghosts.
Speedy Spirits are only found when a room is dark. Luigi should search everything in a room carefully before turning on the lights. Also, the length of time they are stunned by the flashlight is the shortest of any ghost. If Luigi doesn't uncover a Speedy Spirit and the lights turn on in the room, they will be gone forever. Also, if Luigi uncovers a Speedy Spirit and fails to catch it, it never comes back, even after the blackout. Luigi will also be unable to catch the Speedy Spirit if it is defeated via elements.
A Speedy Spirit also appears in Mario & Luigi: Superstar Saga in the Starbeans Café as a representative sent by Professor E. Gadd to taste a new drink.
They are the equivalent of a Gold Greenie from Luigi's Mansion: Dark Moon.