I usually pick up red trinket as support, since my sightstone fills my ward quota, but it feels very lackluster to me. Its only purpose (unless you are against a teemo, or another champ with invisible units) is to nullify the yellow trinket, which isn't even a 100% thing. If you mistake where they warded, you now have no trinket until its off cooldown, and they still have their ward giving them vision. Also, you are able to buy a pink ward for 100 gold, which does the job much better than the trinket (gives vision for longer, possibly indefinitely, and provides vision). I just don't see how it is able to compete with the other two trinkets in most games.
A possible solution to this would be to make the cooldown half the time of the yellow trinket. This way, you would have a bigger chance of taking their ward down, and it also wouldn't be so devastating if you used it on the wrong bush. It would not be too strong, as they can easily trick you into wasting it by walking near a bush and then walking back (making it seem like they warded). I think this would be a good buff to the trinket to consider, making it much more desirable over yellow or red trinket.