Statistically people who do commit don't leave a note at all. ( since a majority of CTBs are a in the moment kinda thing) So I'm gonna follow their lead to increase my odds (:
I don't care to be remembered because I won't even be alive.
I wrote a long ass vulnerable note myself. I explained my entire journey, life philosophy, time spent in isolation, whatever else cause my brain kept nagging me and I was gonna print it, and then pin it on my student dorm wall. But I think I just realized it's kinda meaningless. Others failed you, they didn't do shit to help, at least in my case.
Therefore, why on earth would you need to explain yourself to anyone? They will disregard it anyways, ignore it, not give a shit, misunderstand it, say things like "Oh yeah they were so sick, if only they tried to find help." I cannot imagine a version in which they would deeply understand your reasoning even if you mention it in explicit detail, like what I did in mine.
Also I guess you also can't SEE the results after or be deeply concerned others didn't understand you since like they didn't get it in the first place, they're definitely not gonna do a 180 and put their thinking caps on to start understanding you more deeply after you leave.
But I think what OP mentioned in his case is totally fine though since its a practical request as well to take care of his pet.