Don't play this in ranked! (Unless, I suppose, you practice it and it actually works really well for you.)

I was just theorycrafting my idea for a Twitch Support build, and wanted to write it down. I haven't tested the build yet.

Ignite is probably just as good as Exhaust, however, Exhaust has the double benefit of applying Stoneborn Pact as well as being able to be used to peel or slow an enemy to keep them from escaping.

So Exhaust is a bit more versatile, but if you think you can cheese some people, take ignite. Ignite + E damage can really surprise people sometimes and kill them when they don't expect to die.

Eye of the Watchers for gold/vision. You could also stick with Spellthief's Edge and Sightstone and then sell the Spellthief's later.

Berserker's Greaves for movement speed and to apply more stacks. Could go Mobis or Swifties if you are roaming and ganking.

Black Cleaver to shred your opponents' armor for your team. Don't go this item with an AP Bot laner like Ziggs. Also gives some health and movement speed for better/safer ganks from stealth.

Frozen Mallet is applied by your ultimate in a big AoE and also helps you peel for your teammates.

Runaan's Hurricane is a great way to apply your passive, your Ult, and your Frozen Mallet to more targets.

Your last item is the most situational, since it's rare you get to 6 items as a support. You may try going for more damage, in which case Blade of the Ruined King is probably the best choice, as it's a core item on damage Twitch and gives you some sustain. For just damage, Infinity Edge is probably best (your ult AoE crits!).

If you or your teammates are getting blown up, you can go for a tanky item or a Locket.

If they have a lot of healing (like Vlad/Lifesteal Yasuo or Fiora/Soraka or Nami), you can go for an executioner's calling early on, which you would eventually upgrade into a Mortal Reminder.

Zeke's Convergence is another promising item you might try.

Max W for slow, E for damage. If you find yourself snowballing, you might want to go for E max first or put a few extra points into it.

Stoneborn Pact is going to be better for your teammates. They will heal for more than you could do damage with your support income. However, if you feel like you can carry and build damage items, (or maybe you just don't trust your ADC), you can take Fervor for the extra AD, and go 18/12/0

More attack speed = more stacks of your passive = more true damage. Also, a bit of movement speed seems like a good idea since you're all about sneaking up and catching people out as Twitch.

I'm not very good at runes, so these might be bad, but they make sense to me.