I think you’re confusing with Ethiopian.
Looking for reports for TLV-North America. They seem to have some good prices for the summer.
Absolutely not confusing EgyptAir with Ethiopian Airlines. The Cairo to TLV leg was operated by Air Sinai. It operated as a 'paper airline' for parent company Egyptair under a wet lease-like agreement to serve flights exclusively between Egypt and Israel.
It didn't show up on the online travel sites, except on travelstart.co.za, booking directly with travel agent, or via EgyptAir office. When I flew in 2013, JNB to Cairo was operated by brand new Airbus A330-300, while El Al was operating direct flights to TLV on their extremely ancient 767 fleet which they finally retired in 2019.