Displays menu bar item - stop pulsating please!

I use my iPad a lot as a secondary display for my MacBook Pro when on the road. In Sonoma, when the iPad is connected, the display menu bar item now slowly pulsates from black to gray continuously. I find this constant movement in the corner of my eye distracting and frankly rather annoying (not to mention utterly useless)

Is there a way, short of removing it from the menu bar all together, to make it static again?

I need it the menu item to connect the iPad, as auto connect also connects when I have a real secondary display, which is not what I want.