Eh, the build wasn't exactly in order since that tends to change from game to game. Just figured I would post a typical final build for the sake of brevity.
I typically don't upgrade Targon's Shield to Face of the Mountain until I've finished Iceborn Gauntlet and Aegis of the Legion. The shield is nice, but I mostly get it for the gold generation and sustaining my ally early.
I view Frozen Heart vs Iceborn Gauntlet as personal preference on Taric, personally. While Frozen Heart offers a bit more armor, CDR, and the attack speed slow, Iceborn Gauntlet offers a slow field (for peeling) and Spellblade. Considering Taric's passive, he can constantly proc Spellblade by rotating his abilities to output a lot of damage. This lets him kill anyone trying to get at his carries and 1v1 a lot of champions in the game.
I don't typically get Thornmail on Taric support unless they have a lot of autoattackers. The enemy champions don't want to be focusing me anyways and I'm usually peeling for my carries instead of diving theirs. I know that it's great for dueling or zoning autoattackers (I get it on most tanks and Taric top lane), but I prefer Randuin's Omen for the strong slow it offers and general survivability.
Mikael's is a good support item, but I'm not a fan of it personally. I find that my ally is typically dead inside the duration of the CC or I take too long to cast it. Righteous Glory is strong for engage and I've tried it, but I still prefer Randuin's Omen.
I never finish Ruby Sightstone until my last item is finished or I desperately need the immediate health boost and can't afford/fit anything else. Just not really worthwhile to upgrade beforehand.
I view Taric less as a second tank and more as a second bruiser. You don't really have the CC (Nautilus, Leona, Maokai) to play purely as a tank, but you provide a lot of auras and DPS (due to Spellblade and your passive). I typically like acting as a bodyguard for my carries, debuffing and killing anyone who attempts to harm them while protecting them.
Thank you for the advice though. Always good to see another Taric player.