28:7 and 20:39 both use اليم without a name. 20:39 says the chest will be cast by the water onto the shore where an enemy picks it up; still no name, no country. If we put a pin on any river we are adding what the verse does not say. I propose the moment stays unpinned and the evidence panel records the silence, with any proposed identification shown as grade C or D on the wiki rather than on the map.
Born, placed in the chest, sent on the river
His mother is inspired to nurse him and, when she fears for him, to cast him into the water without fear or grief, with the promise that he will be returned to her and made one of the messengers. The household of Pharaoh picks him up. Nothing beyond this is stated: no name for the river, no date.
Raised in the house of Pharaoh
Pharaoh's wife asks that he be kept; his sister follows him; he is returned to his mother to nurse.
The city and the killing
He enters the city unnoticed, intervenes in a fight, and a man dies. He regrets it and asks forgiveness.
Flight to Madyan
Warned of a plot, he leaves the city in fear and sets out toward Madyan.
The well and the two women
At the water of Madyan he waters the flock of two women who were holding back.
Years of service
He agrees to serve eight years, or ten, for marriage to one of the daughters.
The fire and the sacred valley Tuwa
Travelling with his family he sees a fire, approaches, and is addressed in the sacred valley, Tuwa.
The staff and the hand
His staff becomes a serpent; his hand comes out white. Two signs.
Before Pharaoh
With Aaron he is sent to Pharaoh with the message.
The magicians
The magicians are gathered; the staff swallows what they cast; they fall down in belief.
The signs
The years of drought, the flood, locusts, lice, frogs and blood.
The sea
The sea is parted; Pharaoh's people are drowned in اليم.
The forty nights
Thirty nights completed with ten more; he is given the tablets.
The calf
In his absence the calf is made; on his return it is burned and scattered in اليم.