Why is my second Thunderbolt display not working after Sequoia 15.8 update?

first, can you confirm which displays you are using?

There are TWO displays, commonly mistaken for each other that appear to have a Thunderbolt-2 interface.

The Apple Thunderbolt Display 27-in A1407 is a 2560 by 1440 display that has a lead in cord with ONLY TWO connectors -- Thunderbolt-2 and MagSafe.

This display works great with the Apple ThunderBolt-3 <-> Thunderbolt-2 adapter, US$50.

In addition to the built-in Thunderbolt cable, the display also has a built-in MagSafe-2 connector that charges an older Thunderbolt-equipped MacBook Air or MacBook Pro.

from:

https://everymac.com/monitors/apple/thunderbolt/specs/apple-thunderbolt-display-27-inch-specs.html

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Cinema display LED 27-in A1316 from 2011 is a 2560 by 1440 display that features lead-in cord with three connectors -- Mini DisplayPort, MagSafe-2 and a USB-A pigtail. It does NOT work with the Thunderbolt adapter, but works fine with a USB-C to miniDisplayPort adapter.

It includes three USB 2.0 ports and a convenient single cable with THREE connectors (Mini DisplayPort, MagSafe-2, and USB 2.0), a built-in iSight camera with a mic and a 2.1 speaker system.

This display works great with a USB-C to MINI-DisplayPort adapter.

from:

https://everymac.com/monitors/apple/studio_cinema/specs/apple-led-cinema-display-27-inch-specs.html

What happens when you connect ONLY the most troublesome display, by itself?

You did not cite any case where that one alone lights up, suggesting a possible display failure.

if you have some reason to believe yours has failed due to problems with the captive lead-in cord’s Thunderbolt-2 connection, Users have successfully connected a discrete Thunderbolt-2 cable to the second Thunderbolt-2 port (on the chassis) and had the display work fine.