Aside from pull and push - there's another model of information. Ambient. The Ambient orb ( http://www.ambientdevices.com ) was one that kicked it off many years ago. Clocks are the classical version of this. I've got a hue light that has its intensity in the morning a function of the snowfall over the last 8 hours (do I need to shovel now).

Not everything needs a button.

That said, for the button... if it takes more than a few minutes to reconfigure a dash button, consider an IoT button https://aws.amazon.com/iotbutton/ that already does the arbitrary integration.