The Red Gyarados was my first shiny, and my only one (save my Red Version Blastoise that ended up having the right IVs to be shiny) for some time. I could tell it was different and special, since it was a stand-alone Pokemon that you had to approach to encounter (like legendaries from RBY), but I can't remember if I was playing on a GameBoy Color then, or still on GameBoy Pocket. If the latter, I wouldn't have noticed the color difference, but would probably have noticed the stars and recognized that, as an approachable, special Pokemon, it was important enough to save beforehand and try repeatedly to capture if if needed. I captured it (presumably without much trouble, since I have stronger memories of the Pokemon I struggled to capture). I think I used it for some HMs, like Waterfall and Whirlpool, and stuck it in my team against the Elite Four the first time, but it wasn't part of my regular team. I initially played through Gold as a solo run with Totodile (who I didn't want to evolve because I thought Croconaw and Feraligatr were ugly), and I needed some spare Pokemon to serve as cannon fodder while I healed Totodile throughout my battles. After that first victory, though, I put the Red Gyarados in my PC, built an actual (albeit imbalanced) team, and didn't think about it too much again (except to lament my lack of subsequent shiny encounters).