nohup is also useful for this situation, but a lot of people don’t seem to know about it!
In those cases, I've found dtach to be slightly more reliable than nohup. Frequently I'll try one and switch to the other. Less frequently, I'll correct users' configs/workflows that are necessitating the troubleshooting in the first place. Even less frequently, I'll dig into what was actually the issue :)
https://linux.die.net/man/1/dtach https://dtach.sourceforge.net/
[1] https://github.com/nelhage/reptyr [2] https://github.com/lkundrak/retty
Implying "tail -f $LOGFILE" is akin to tmux reattaching to a console is a stretch.