There are several options where you can store your luggage in Eilat.
Luggage storage at the Central bus station
One of these options is luggage storage at the Eilat Central bus station.
Address: 12 Sderot HaTmarim, Eilat
Unfortunately we don't have any information about baggage storage price there.
Luggage storage is not automated, for every piece of luggage you will have to pay separately.
Eilat Central bus station on map:
Automated luggage lockers
There are automated luggage lockers not far away from the bus station. Payment will be for a whole cell, not for each luggage item separately (as it is in the bus station).
One cell price: 10 shekels for 24hrs.
If you close the cell and then open it, you will have to pay the money for re-storing the luggage (if you need to close the cell again).
Fine of 200 shekels is determined for loss of the key and for exceeding the storage time. After 24 hours of storage at exceeding time limit the company is not responsible for the luggage.
Address: Sderot HaTmarim 45, Eilat, Israel