Are they looking ahead? Are they prepared to act? How is their timing? All of this and more is what you can learn about someone by observing how they react to another driver’s acceleration.
To take it a step further, you can also read and learn about how others react to that person’s reaction to the initial individual’s acceleration.
For example, if someone unnecessarily accelerates or accelerates too much, is the person following aware and doesn’t over-accelerate too? …How about those observing them? How is their awareness and timing?
Again, the more aware and more skilled a person is, the better the timing of their accelerations usually are, rather than just reacting to the person ahead.