Honestly I don't see why you'd want to stick up for him... What proof do you have of him going afk because he had a headache or he went to get something to stop it??
If he got kicked for too many warnings that means he broke too many rules which is again his fault.
The spectator mode is there if you do not feel like playing or going afk or just watching others play so it is his fault for not going into spectator mode, there isn't an excuse for that.
Another point someone made was that why didn't he just wait for the round to be over and do it on runners? But Timmy had been death at least 3 times already and if you have a headache and are looking at any screen, such as TV or computer, your headache usually gets a lot worse. Also, if you do it on death and you know you won't be gone long then you know you can put your faith on your team without worrying about whether you will die or not (for afk-against maps or anti kick for afk).
So he has a headache and yet he came back to his computer looked at his screen and saw he got warned so I don't really think what you've just said makes sense if he has came back to play.
This is a dumbass excuse to be fair, why would he not notify an staff member who was on the server that he has to go afk?
If I was still staff on Deathrun and someone had to go afk as death if it was important or they had to go I'd be alright with that as long as they told me. It's his own fault for lack of communication and breaking many rules that lead to his ban, there is no point in sticking up for him if you have 0 proof to back up what he claims happened.