Wait what kind of timer??
A countdown timer that goes down or one that you have to beat and goes up
Personally I think that a countdown timer would be a good option to have, cause the game is quite fast paced and I think it could add that extra bit of pressure on the player. But that might be too much pressure (maybe have it as a selectable option if you can do that). The idea of a counter you have to beat so it gives you extra time would maybe be the go to one if you want to give the player SOME breathing space, but still force them to keep up the pace. TL;DR depends on how much pressure you want to put on the player, I think most people would prefer option 2 though...
its already out https://squid-goodman.itch.io/escape-scarlet-prison