Currently, to see any information about a RW you need to go into the faction page and check.
The only notification that a RW is set start is on the events page, and whilst I find experienced players obviously take note of this, it can easily get caught up in the logs for newer players who don't know what's going on. A status icon as a reminder for them to sort their affairs out beforehand via prepping to contribute or travel would be helpful.
Additionally, it would just be great to keep on doing what you're doing without navigating to the faction page. Hovering over the status icon could be dynamic in telling you when it's starting, and when it's begun, the current score, lead target and duration.
I feel like this would be a great addition and make life a whole lot easier in a few different ways.