What is the Eights on Pylons maneuver intended to demonstrate about a pilot's skillset?
The maneuver tests the ability of the pilot to hold precise altitude and airspeed. You need to make constant small corrections when flying into and away from the wind. In my opinion, it is the most difficult of the Commercial maneuvers.
Garry Wing has a good explanation of the technique.
As Garry Wing explained in the video. If you don’t hold precise altitude and groundspeed the point moves. So as the wind increases upwind it lowers your groundspeed requiring a lower pivotal altitude. Downwind you will increase your groundspeed requiring a higher pivotal altitude. So you need to remain coordinated, constantly vary the altitude, scan for traffic, and maintain situational awareness of your location around the pylons.
Your airspeed will vary a bit as you climb and descend and head into and away from the wind, but if you can’t maintain a consistent groundspeed your pivotal altitude will change and that will throw off the whole maneuver. As you can see in the chart below, if your groundspeed varies by 4 kts from 87 to 92 kts the pivotal altitude changes by 65'. This is the part of the maneuver that requires precise control of airspeed and altitude with coordinated use of the rudder and ailerons.

The FAA explains it well in Airplane Flying Handbook:

Eights-on-Pylons
The eights-on-pylons is the most advanced and
difficult of the ground reference maneuvers. Because of the techniques
involved, the eights-on-pylons are unmatched for developing intuitive
control of the airplane. Similar to eights around pylons except
altitude is varied to maintain a specific visual reference to the
pivot points.
Chapter Summary
At the completion of ground reference maneuvers, the
pilot should not only be able to command the airplane to specific
pitch, roll, and yaw attitudes but, while correcting for the effects
of wind drift, also control the airplane’s orientation in relation to
ground-based references. It should be reinforced that safety is
paramount in all aspects of flying. Ground reference maneuvers require
planning and high levels of vigilance to ensure that the practice and
performance of these maneuvers are executed where the safety to groups
of people, livestock, communities, and the pilot is not compromised.
To master ground reference maneuvers, a pilot must develop
coordination, timing, and division of attention to accurately maneuver
the airplane in reference to flight attitudes and specific ground
references. With these enhanced skills, the pilot significantly
strengthens their competency in everyday flight maneuvers, such as
straight-and-level, turns, climbs, and descents.