So my issue isn't exactly the same but I stumbled onto this forum post googling so thought I would at least add what I discovered.
***TLDR:*** Make sure the power connectors are tightened down completely - you will get weird behavior that doesn't necessarily trigger the diagnostic LEDs.
[image|2849549]
***Long answer and discovery:***
In my situation the machine worked fine - booted up, worked under heavy load for hours (cinebench + unigine + geekbench 5) however, when the machine would sleep and wake itself up periodically to run time machine backups etc. (whatever its doing when PowerNap is enable in Energy Settings) it would every few days crash and reboot. Sometimes I would catch it and noticed that in Macs Fan Control the fan rpm would be 0 which is suspect and made me think the machine was randomly overheating due to the fan not spinning. Sometimes the fan would self-correct and start spinning though and my thought was that maybe the Fan was going bad and so I replaced it (the entire top housing with the fan + wifi/bt card etc) but this did not fix the issue.
Next, I opened the outer case of the machine, put a [post|158924|magnet near the back I/O panel|new_window=true] so I could boot the machine and started following this [link|https://logi.wiki/index.php/Mac_Pro_6,1_Late_2013_Diagnostic_LEDs|wiki|new_window=true] and checking the I/O board diagnostic LED which were all fine (pressing the little button I got 7 green LEDs which is good). Next I checked the CPU Riser card/board (the board that actually has the RAM and CPU connected to it) and the LEDs were all off during boot up (there is no button for this board) so this was also good.
At this point I wasn't sure what the issue was so I put the outer case/housing back on and then put it under more stress tests (cinebench etc.). This time I noticed something weird which was a smell from the machine but I figured it was the used fan I had replaced which was a bit dusty.
I took the outer housing off again and disconnected the top housing/fan again so I could look downward into the machine. Then I booted up the machine (magnet attached etc) and noticed a yellow light now on the CPU riser card at the bottom of the machine (power problem I think) and no output to the screen. Then I realized right in front of me the little grate over the PSU connectors was actually melted!
[image|2849547]
This concerned me given I had not messed with this grate during the fan replacement however I had self-upgraded the CPU over a year ago and had to disassemble the entire machine. When I removed the grate, I noticed that 3 of the screws were not tightened down completely AND there was melted plastic between the screw head and the flat connector, resulting in a faulty electrical connection between the PSU and CPU Riser board/card.
The weird thing about all this was that the power issues only manifested themselves when the machine transitioned from sleep to wake or from sleep to darkwake but not under full system load at least until I had replaced the fan. My guess is that these screws have been lose for a year and when I replaced the fan, I jostled it just enough to make the connectors really disconnect and result in a yellow LED power issue on the CPU riser card/board.
Anyhow, this was a weird one but ultimately my user upgrade error. Hope this helps save someone else time in the future.