Why Evelynn support? Well being a support main I've become bored of the typical support champs, I also wanted to improve my mastery on Evelynn, and I found playing support to be the best way of earning S ranks. It does work but you have to really rely on your adc and team. I wouldn't advise trying this in ranked until you're really comfortable playing Evelynn support and don't mind the entire team reporting you if you loose or have a bad match.

Proof that it works
Some advice for getting S rank is lots of wards, and get more CS then I do, all my scores are really low in CS.

Eve support is really fun, creeping up on squishy supports from behind is probably the best thing you can do on league. So I hope this guide helps you if you want to try it.

Pros-

Really fun to play

Can act as a second jungle which leads to more ganks for everyone

Puts pressure on lane

Not many supports/adcs know how to counter

Can turret dive for kill secures

Great mobility with boots

Destroys squishy supports and adcs

Cons-

Really squishy if you cant afford morellonomicon or rylei < as these should be your last items

Team will flame, report and troll (ive had people play supports as jungle because ive chosen a jungle as a support, and then feed, people will also ban Evelynn because they think you're trolling) People will also report you if the game goes wrong.

Not great before lvl 6, without demon shade you will not be able to get very close to the adc or sup to use W>Q, early game you can poke with hate spike but it doesn't do much damage at that point.

Due to being bad pre level 6, it is likely without a good adc, the enemies will have pushed very far

Not many ways to protect your adc, except exhaust and charm, but charm takes time

Terrible against tanks and roots

You must take flash, but for your second summoner spell you have two options.

Teleport

Lets you return to bot lane after roaming or go to where you're needed fast. This is good when you can't afford boots and need to get places fast, or bot lane is struggling. Also good for back dooring in close games.

Exhaust
I personally almost always take exhaust, the slow from exhaust combined with mobi boots allows you to catch up to enemies and ult or use whiplash. A good gap closer, but it also helps protect your adc, you can use Exhaust to slow enemies when they're chasing your adc and reduce their damage. You can also use exhaust on enemies that are chasing you, to slow them down and give you hopefully enough time to run far from them and hide in demonshade.

You want to start with spellthiefs edge, alternatively you could take relics shield if you want cs.

Poke the adc with hate spike as often as possible to get gold from spellthief, but be careful as hate spikes range is less then most sups/adc's skill range, so either be behind minions or wait for the sup to use their spells first.

At lvl 2 you want to unlock allure so that you can charm the sup or adc, whichever is more squishy and charm them towards your adc.

Gank other lanes when you can, as Evelynn support you do not want to stay in bot lane for long unless your adc is doing incredibly well, if they're 0/6, you should roam to become stronger and help them later. As Eve support you want to be constantly on the move.

After level 6 you should see if you can roam and help other lanes, and then return to bot lane when your adc is struggling or when you're falling behind in levels.

Look for sneaky opportunities to attack enemies, such as if you see an enemy jungler on low health from a camp, but do not attack enemies alone, unless they're low health or you're feeling confident. I often gank mid, as its close enough to quickly return to bot.

Very late in a game you can follow behind the team and ult whenever an enemy tries to escape under a turret, and help with drakes/objectives when you can, keeping in mind that turrets reveal you

You can take any items with ability power, though some are stronger then others. Your first back should either be a sheen, for quicker cooldowns, or a fiendish codex. If you have spare coin always get a control ward.

Late game you always want spellbinder for the speed boost which helps you escape and chase.

Rabadons death cap is great if you can afford it, this can be built last but with items that form it bought earlier in the game.

Boots should be secondary to ability power. Boots are great but useless if your abilities do no damage.

I hope you find this guide useful, although being good at Evelynn support takes practice and some previous knowledge playing her as jungle will help.