Mac Pro 2013 no video on restart.

AFAIK, there is no way to downgrade the firmware even by Apple or an AASP. A firmware update on a Mac is a permanent update.

Edit: The 2013 Mac Pro is known to have GPU issues. Even though the issue is supposed to be limited to a certain GPU with certain Macs I have found the issue exists with all of the GPUs on the Mac Pro 2013. The issue I have seen usually involves GPU Kernel Panics, but IIRC there are other symptoms of a bad GPU for this system.

If you have multiple displays or Thunderbolt devices connected, then try to put them on different pairs of ports. The top left two Thunderbolt ports are linked as are the top right two ports, plus the bottom two are linked together. IIRC the HDMI port is connected to the bottom Thunderbolt ports.

https://help.uaudio.com/hc/en-us/articles/115005146946-Mac-Pro-Late-2013-Thunderbolt-Optimization

If it is a GPU issue and as long as Apple replaces both GPUs, then it would be Ok to repair it. However, when we had confirmed intermittent GPU Kernel Panics replacing a single GPU did not solve the problem and Apple wanted us to pay for another GPU. IIRC each GPU costs about $300 US just for the part so labor & taxes will add more. That is a lot of money to "guess" on a repair if only a single GPU is replaced.

At one time Apple had a free repair program for one of the GPUs (now expired) which they replaced both GPUs at the same time, but outside of that free program or with another model of the GPU Apple only replaces a single GPU at a time which isn't good if the problem is intermittent. Our organization no longer replaces the GPUs on the 2013 model since Apple cannot guarantee the repair if the issue is intermittent (assuming they even reproduce the issue in the first place). We now only use these Trash cans (very fitting name) in non-critical areas since almost all of them have GPU related Kernel Panics from time to time.

FYI, the first part to replace for the no video issue is the GPU B Board according to the Apple Service Guide for this unit. One GPU is more dedicated to video than the second one. These GPUs do not work exactly like you think they do.

However, like I said in my previous post I have seen many of our organization's 2013 Mac Pros have video issues that did not qualify for the free repair program (now expired) which was supposed to have affected only certain D500 & D700 GPUs for a small time frame. However, we had Mac Pros built outside of that time period and even using a D300 GPU which had identical issues to that covered by the free GPU repair program (95% of the time they all experienced one of two types of GPU related Kernel Panics). Here is an article with some of the details about the GPU issues associated with the 2013 Mac Pros:

https://www.macrumors.com/2016/02/06/late-2013-mac-pro-video-issues-repair-program/

Also like I said our GPU issues were not completely resolved by replacing just one GPU. The issue occurred less often, but the GPU issues still continued. There are also other parts that could contribute to the issue such as a defective internal GPU cable or I/O Board. If your issue is intermittent, then Apple may think they solved the problem, but later you find out the issue still exists. After what our organization has experienced with these Trash Can GPU issues we no longer waste any more money on this crap system. Perhaps since your issue is more reproducible you will have better luck at a good complete repair. Just be careful.

Hey there fuzzy561,

We're sure you're eager to get your Mac Pro up and running as expected. You've done a great job isolating and troubleshooting thus far. Since you've isolated the issue to the hardware components and the macOS software, it might be a good idea to have the Mac inspected by a technician. The Apple Support team can help you explore all your options.

Get Support

Cheers!

<<I would be surprised if it was a gpu issue unless they both failed at the same time.>>

On that Mac Pro, ALL six display-generators are on ONE of the graphics cards. The other card is solely for GPU Computing, and has no display-generators.

Huh...

I've just bought an SH Mac Pro Late 2013 full options...

It had Catalina, but I've updated to the latest Big Sur...

Big Sur is working, But I had the "great" idea to clean the cooler, as it was really dirty.

All ok, and I've begun to install a lot of software. One software requested a reboot and after that, I got no video signal (TB 2 or HDMI).

Now I search on google for answers.

Your reply gives me hope, so I'll open tomorrow the crash can and push all connectors.

If they can fix your currently non-working high-powered computer, it will be worth the Big Fee. A new Mac of that class starts at about US$6,000.