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Your description of it as a "vivid ruby red star" might indicate it to be a carbon star. However, how red a star appears depends on many factors:
where it might be in its cycle (carbon stars are generally variable stars), how low it is in the sky, the transparency of the atmosphere and the actual optics of your telescope+eyepiece.
Carbon stars generally have a B-V colour index greater than 2. For example V Hydrae has a colour index of 4.5, Hind's Crimson Star (R Leporis) has a colour index of 3.5. DY Crucis (Ruby Crucis) next to Mimosa has a colour index of 5.8.
There don't seem to be any "bright" carbon stars within cooee of theta Centauri.
I can only find a few possible candidates and they are all around 11th magnitude.
TYC 7288-1528-1 (14 03 37.36, -34 59 37.8) has magnitude 10.78 and colour index 2.49. It is about 1.6 degrees from Menkent.
TYC 7288-1181-1 (14 06 16.56, -34 50 09.5) has magnitude 10.92 and colour index 2.14. It is also about 1.6 degrees from Menkent and about half a degree from the previous star.
A redder star is TYC 7803-0011-1 (14 04 37.71, -37 35 18.1), magnitude 11.12. It has a colour index of 3.41 but unfortunately is 1.3 degrees from Menkent in the opposite direction to Hydra.
Regards, Rob
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