this is pre-hipster-triumph but post initial triumph shut down.
Triumph opened up again and produced a line of triple cylinder bikes that are not very well known, mostly referred to as the classic triples. i'm not sure the trident falls in to that category, it might have been in the sportier group with the speed triple and daytona. but they all shared the same power plant just slightly altered.
My first bike was a 2000 triumph adventurer. i loved it. it was my first bike so i couldn't really compare my impressions of it to anything. reliability was excellent, just sometimes some dumb things would go like the neutral switch. The carbs/airbox were a pain to get off. if you removed the sprocket cover you had to either have the bike tilted or change the oil. The pushrod seal was prone to leaking.
otherwise, they were bulletproof and it was a beautiful bike.
i later wished i had a Legend or thunderbird / thunderbird sport for a more standard set up.
Head over to triumphrat.net there's a great bunch of guys in the classic triples area.
I think one of more significant issues with the bikes was the sprag clutch and earlier models had mikuni carbs that were garbage (may or may not be on the trident, idk).
if anyone in my area gets curious about these Tridents, I stumbled across one the other day on DC's Craigslist i think. couldn't believe it.