After talking with Milo at World’s, my kid learned about a mechanism to run two functions on one motor. He has flirted with the idea of making a video, crediting Milo for the inspiration. I will see if he still wants to make that video, he is working on another one at the moment.
Do you have a motor being used and dedicated for the blue dispenser only? You could use a pulley system that loosens the tension on the extension arm as the blue moves backwards (Relative to the blue), and then you can use a rubber banding system to propel the arm outwards. The string can tug the arm out a little bit, and the rubber bands can do all of the real work, but neither system can fully pull it out by themselves, alas, a hybrid system will work rather well. That’s currently what our team is using and it works great.
Here is a video of a direction switcher (not my video). I built one of these a while back, and it seems to work nicely. The only con is that each side can only move in one direction; otherwise, the mechanism will switch to the other side. The video isn’t the best quality, but I’m sure it will click if you look at it enough.