The star has been located (until somebody finds one better):
=Wolf 294=
Location: RA: 6 hr 51m 35s. Dec.: 33, 20.
Constellation Location: Gemini
Distance from Sol: 19.4 light years
Spectral Class: dM4
(dwarf red star with no emission lines, i.e., not a flare star--they erupt, which would probably cause problems at habitable planets)
The arguments in favor:
--red star as per text re: pink light, no blue output from star.
--a Wolf star (that isn't a flare star).
--less than or equal to 20 light years from Sol.
--(special bonus) located in the constellation of the Twins.
Your Copernican Correspondent turned crispy critter,
=mantis=