Neutralize Poison rules?
Then what I have introduced may be helpful.
Poison does damage over time. Roll for damage, roll for time, start the poison. Simple, and it is even realistic.
For example, in my Kids D&D campaign, a poison dart hit the thief and she failed her saving throw. On the fly I said it gave 1d6 damage over 1d6 rounds. I rolled in secret 2 damage, 3 rounds. She had 6 hit points. First round 2 damage. She panicked, took healing. Then 2 more damage. She waited. Then 2 more damage, more healing taken. No more damage.
Player anxiety, time to heal, no save or die. I am going to use this mechanic for all my poisons. Easy to scale up or down depending on strength of poison eg 1d10 damage over 2d6 rounds.
No healing available, time for that farewell speech. Unless one likes, "Black Dougal gasps 'Poison!' and falls to the floor. He looks dead."