How To Fill My Down Time As Support

This depends on what part of the game you're in.

During laning, if your ADC went back to heal or buy and won't make it back to lane in time to kill the current minion wave, then go ahead and last-hit those minions yourself. It's much better than wasting the gold. You can also leave lane briefly to ward nearby brushes and such to make your lane safer.

In the later game, your job is vision control. Make sure that you can see baron and dragon if they're close to coming back up, and that the enemy team can't. If you can, try to get vision a little bit past your safe front, so that you can see what the enemies are up to. Whenever your teammates aren't around to support, your job is to control vision (including denying your opponents' vision) without feeding the enemy team.

I'm a main support player and I can tell you: there are times where you will seem "useless". But note the word seem. The supporter is arguably the best position in the team for awareness and play making. It's your job to keep an overview of the whole game since you are the one that only comes to action when you're about to kill something. Top/Mid and Adc will have to worry about CS while the jungler has to control his jungletimers and ganks (although the jungler is also very good at awareness).

Note also that there are 2 types of supporters:

As a harrassing supporter like Lulu/Annie/Thresh you will be focussing more on denying the enemy Adc farm or as already mentioned you try to harass him.

As a Passive or PassiveAggressive supporter you will either only safe the hp bar of your adc (Soraka/Sona) or in the case of an PassiveAggressive supporter you will only go in when You're about to make a kill or you gotta save someone (Leona/Blitzcrank/Alistar).

Keeping an eye on the map is of course easiest when playing as an Passive(Aggressive) Supporter, but this also includes the "I'm bored" or "I'm useless" moments.

For when your ADC backs off his lane you can go back aswell and spend your gold on wards/items, you can stay and CS so no creeps get lost or you can Gank other lanes. Since most supporters have really high amount of CC or Utility a gank can be fatal. Especially when combined with your jungler. A triple gank mid with Nocturne, Leona and Brand is really hard to survive unless everyone of these 3 misses their skillshots.

The ganking part can also be applied when your adc is really bad. If you think kills on your Adc will be useless since he can't position himself late just gank mid. Try to figure out who can carry this game.

Oh and last thing of course to do: Ward ward ward. One of your main jobs as a supporter (I don't like it either...)