Hello there, JDBartram.
The following Knowledge Base article should help you:
Thanks for reaching out to Apple Support Communities.
Thank you Pedro D.,
I had tried this before, but tried it again several times. The Thunderbolt Firmware Update still appears in the App Store.
I also tried the suggestions by rkaufmann87 as best I understood it, at this thread:
This did not make any difference either.
Is the firmware installing when you restart? You will know because there will be a long tone and then a progress bar running across the screen. If you've never seen that, then the firmware hasn't been updated.
Your Macbook Pro must be connected to external power for the update to run. It will not install on battery power.
There is a progress bar which says "Instaling Sofware Update" after I click on 'Restart', but there is no long tone. I just tried this (again) both with and without the external display which is connected with the Thunderbolt port.
Meant to add that the problem still exists and that the laptop is plugged in and the status bar shows Power Source: Power Adapter.
I can't remember that update (if I had it), but what you describe sounds like normal updates that must be installed after restart, not a firmware update.
Now, it may be that the Thunderbolt firmware doesn't have that same behavior.
When that is done installing. Shut down, then press the power button to turn it on. Don't hold it down, just press and release. See if you get a gray screen with progress bar.