Just escaped Bronze myself as a support main. There are a couple things that I try to focus on outside the usual "do your damn job" categories like you mentioned:
Don't just stick to your ADC for the whole game, especially if there is a carry on your team that would benefit more from your help. Once the laning phase is over, you are just as free to move about the map as anyone, and choosing who to support at critical moments can turn a game on its head. Being able to read what your opponent's next move is absolutely critical to this point, because that's how you're going to know where you'll be needed most. You will learn this through experience, but you can also watch streams to get the inside track on this. That being said, turret sieges are an ADC's specialty, so making sure they can safely get shots on the tower/inhib is pretty important, not to mention that your ADC may be the carry I referenced above.
Depending on your team comp, sometimes it actually works to play a champion you can carry with yourself. I know that sounds anti-meta and goes against what a support is supposed to do, but the thing that is most important is finding a way to bring your team to victory, in whatever form that takes. Zyra support is still really strong and a prime example of this, but don't think that it has to be a high damage support; I've carried more games as Nautilus support than any other champion. The trick here is knowing your champion pick inside-out, including matchups.
The biggest asset I think whenever you are trying to advance in ranked is patience, particularly for a support main but for anyone in general. You will not win them all, and all games are not necessarily lost just because your team is down 6+ kills at 10 minutes. Patience will teach you how to play from behind and how to take only the fights and contentions that you can win.
Keep your head up, though, mate. It'll come to you if you are persistent and constantly learning.