Down can be used phrasally/adverbially to indicate the intent/effect is to prevent the object from moving--especially if the context involves the verbs or meanings of tie, strap, tape, bind, bundle, etc.
Likely the most common example is tie down - if you tie down the boards on the truck - we expect the boards won't be moving when the truck does. Similarly, taping something down means we don't want what we are taping to move.
Up in these contexts will mean to get a bunch of X and keep it bundled. So if you tape up X or tie up X - you are trying to prevent X from falling apart or get separated. If X is a person, animal, or something that can move by itself, you are more concerned with not allowing X to escape, but they might still be able to move somewhat.
Off means to separate a portion of X from another portion. So you might tape off a wall to prevent paint from getting on one part of the wall, or tie off a thread while sewing to separate the part on the stitch from the dangling thread.
Without down, up, or off - unless context is strong, you're being vague. Examples: If you taped a wall as opposed to taped off a wall, it means you literally just put tape on the middle of the wall and the listener/reader will be wondering why. If you tied some boards on a truck - did you slap a string around each board for some reason?
The rough edges of the hole on the wooden wall were taped down in order to prevent splinters of wood to hurt your hand.
Here, I would use taped over - because over specifically means "to cover." But honestly if the edges are really scraggly and splintery and the holes are large, then taped down would work too.
Best Answer
I think the simplest, yet most idiomatic way to say that in English would be this:
Or, as was suggested by brichins down below, the sentence can be made even shorter:
if it's implied that it is your hands that you're going to use to cover her eyes.