SECCO 1 is an extremely dark, low-mass (M⋆ ≃ 105 M⊙), star-forming stellar system lying in the low-velocity cloud (LVC) substructure of the Virgo cluster of galaxies, and hosting several H II regions. Here, we review our knowledge of this remarkable system, and present the results of (a) additional analysis of our panoramic spectroscopic observations with MUSE, (b) the combined analysis of Hubble Space Telescope and MUSE data, and (c) new narrow-band observations obtained with OSIRIS@GTC to search for additional H II regions in the surroundings of the system. We provide new evidence supporting an age as young as ≲ 4 Myr for the stars that are currently ionizing the gas in SECCO 1. We identify only one new promising candidate H II region possibly associated with SECCO 1, thus confirming the extreme isolation of the system. We also identify three additional candidate pressure-supported dark clouds in Virgo among the targets of the SECCO survey. Various possible hypotheses for the nature and origin of SECCO 1 are considered and discussed, also with the help of dedicated hydrodynamical simulations showing that a hydrogen cloud with the characteristics of SECCO 1 can likely survive for ≳ 1 Gyr while travelling within the LVC Intra Cluster Medium.