Pixel Pulse can give you a pulsing Ambient Display that activates when you have notifications available.
The free option uses a branded icon and repeats the title and content of your actual notifications. The paid version adds the ability to use the default apps icon and colors, override colors, and have swipe and tap actions.
You can also replace the double tap to wake with the scrolling pulse, which is my favorite feature. Just be sure to turn off Google's double tap to wake.
For it to work you need the following settings:
Notification content shown on the lock screen
Always on display off
Wake on new notifications on
*If you previously purchased Ambi-Turner - there is a mechanism to convert your purchase to this app.