Fast Clock

Only the plain Mummy counts. The colored variants that spawn once a desert has been taken over by an evil biome will never hand this over, so a grind in a converted desert is time you are not getting back. Pixies and Wraiths are the other two sources and both are easier to farm deliberately, Pixies on any open Hallowed ground at night and Wraiths on the surface once it is dark.

Slow immunity by itself does not deserve an accessory slot on anything. What matters is that this is half of a pair that eventually rolls up into the Ankh Shield, and every small immunity trinket you are still missing is another farm standing between you and finishing it. Shimmer will flip this into its partner piece, which sounds like a shortcut right up until you remember the combine wants both halves at once.