So, as someone who has been running into problems with the boss timer being correct for me, I would like to suggest that a command be added for this issue. There are many commands, however this will be one of the most useful ones: ~bosstimer. Its main function would be to list the last 3 times of said boss with a date stamp as well.
If you do a search, you can see this has been discussed a couple times before in different iterations: https://royals.ms/forum/threads/boss-timers.69146/ https://royals.ms/forum/threads/boss-timer.57518/ https://royals.ms/forum/threads/cooldown-timer-of-the-boss.50783/
If you're having trouble with your cool down, the next time you enter a boss you could write down the time you entered or make a mental note. This actually helps a lot since you can get ready before your cool down is up and be ready to enter at that exact time.