First, the sentence is in the simple present tense, we know that because the action happens unceasingly: A mummy is always still, it always rests, meaning that is not a temporary action.
Second, "rests" is the correct verb form because in the simple present, most regular verbs use the root form*, except in the third-person singular, which is added and "s", "es", "ies", etc, depending on the verb; and "The mummy" is a third-person singular.
*"Rest" is the root form of the verb.
