I don't want to see it if someone pings my death timer
Most of the time, when someone pings an ally's death timer, it's to flame them for dying. It's pretty frustrating to see someone ping your death timer, and by the time they do it it's too late to mute their pings. And I don't always want to mute pings, even when someone is being toxic, because pings often provide valuable communication.
I can understand why pinging a teammate's death timer might be a reasonable thing to do - you want to warn your team not to fight because an ally is dead, or you might want to ping your own timer to warn your team that you aren't there to help. And obviously it makes sense to ping enemy death timers sometimes.
But I never need to know when someone pings my death timer. I know I'm dead, and how long til I respawn, and there's nothing I can do until then. I don't think there is any situation where I need to be notified that someone has pinged my death timer.
So I propose that Riot make it so you can't see when your own death timer pings, but you can see pings on an ally's or enemy's death timer.
(On a related issue - I understand the desire not to let people ping Kill/Death/Assist ratios (you don't want people to be able to ping the KDA of a player who is doing poorly). But I think it could be useful to be able to ping your own KDA ("I'm super fed, so let's fight" or "I'm really weak, let me get some farm") or maybe an enemy's ("Be careful, this Zed is 7/0"), even if you can't ping an ally's KDA.)