That isn't exactly what they are now providing on a Ring Pro. My Pro Power Kit not only had the 2 wire pigtail but 2 stab connectors. They instructed me to take one leg of the 16v power supply and put it in series with 2 stab connectors (i.e. one stab point feeds in the direction of the Ring and one stab point feeds in the direction of the power supply). Essentially, this is in series of one leg of the power supply. The other leg of the power supply goes undisrupted to the Ring. This was per instructions from their tech support. He explained that it was like a fuse in line between the power supply and the Ring to protect it. He even emailed me a pic of how to connect it

I did this and the pigtail with the 2 spade lugs were unplugged and set aside.
The Ring works fine.

For grins, I plugged back in the pigtail and read with my VOM. The 2 leads of the pigtail don't show any change when the Ring call button is pressed. There is no voltage on the 2 leads either and resistance is appx 4-5 ohms (doesn't change).

If I read one of these pigtail spade leads across the other undisrupted leg of the power supply I read 16v AC with my VOM.

In a typical door chime the front button merely completes the 16v circuit to the attached chime in the house. The Ring needs a constant 16v to function

How are we going to get a trigger out of this? I'm missing something.

Its not that important. I can always get one of their plug in chimes, which are not expensive, But I would like to trigger a door chime module in my Elan system and it would be distributed in the ceiling speakers. I've done this multiple times with clients Elan systems (standard door chime and button push)