Yes, it is legitimate and original, although it is perhaps a little tired after 63 years of wear and tear. If you do decide to buy this watch for your brother as a daily-wear timepiece, you should also consider a complete service by an independent watchmaker who is familiar with servicing vintage mechanical watches.
Based on your pictures, you are considering a steel-cased Tissot T.12 automatic with the "visodate" feature. These watches came in a date and no-date version. This model was actually designed as a skindiver's sports watch - the "12" in the model name refers to the watch's ability (when brand new) to resist 12 atmos of underwater pressure.
The watch movement is Tissot's in-house designed, full-rotor 28.5R-621 caliber. The serial number dates the manufacture of the watch to 1958. The caseback features the engraved galleon, which is actually a relatively uncommon (and very cool
😎) feature for this model year.
However, the T.12 itself is not a rare watch - it was a popular model for Tissot, and they made lots of them. The model line lasted, in different forms and variations, until the 1970s. Considering that you're thinking of it as a gift, you might want to look around for another example in nicer condition. A range of up to $250 in whatever currency you are using is a reasonable price for one in nice condition.