Is Vertical Speed based on True Airspeed or Groundspeed? I have edited this for clarity

For the same angle of descent or climb, does vertical speed increase if true airspeed is greater or if ground speed is greater (due to a tailwind)? 

Imagine a triangle and assume a three degree angle of descent. The hypotenuse represents the flight path. The opposite end represents the amount of descent. The adjacent side represents the ____. Airspeed or ground speed? 

If headwind matched true airspeed, I imagine an aircraft would climb and descend in place (like an elevator) without knowing anything about it's ground speed. However, with large tailwinds, ground speed will obviously be much larger. Going back to the triangle concept--the hypotenuse will be very long--which means the aircraft would descend more quickly. 

Furthermore, every Captain I've talked with swears rate of descent increases with a tailwind. However, I believe this may be a result of reduced tailwinds at lower altitudes. 

Do you have a source or a formula you can cite? 
Thanks.
Vertical speed, as measured by the Vertical Speed Indicator (VSI) should be measured entirely by the changing air-pressure at the static port, and should be completely unrelated to airspeed and ground speed.

The static port is a small hole, (about the size of a large needle or tiny nail) in the side of the airplane, with a pressure-sensor inside.  As that sensor measures a decreasing pressure, it indicates that the airplane is climbing.

An increasing pressure indicates the airplane is descending.

Neither measurement should depend on the plane's air or ground speed.  The sensor should still work even if mounted on a hot air balloon (or other stationary craft).

Source: http://www.boldmethod.com/learn-to-fly/aircraft-systems/how-does-a-vsi-work/