About 15 to 20 years ago you would not have had any problems spotting beaver in the park, that was before the park service began rounding them up and removing them from the park. It is my understanding that the park service no longer does that, and that only distructive beavers are removed. Sadly the damage has already been done and beaver sightings are way down.
The waters over by Duck Brook Bridge still have a few active beaver, the waters right behind that small building before the bridge. You can see the nice beaver lodge out in the water.
One half of the Duck Brook Bridge Road is now closed to cars so to reach the area of the bridge by car you need to drive out on the Eagle Lake road, route 233, and look for The Duck Brook Bridge road on the right..