Firstly it isn't a given that Israeli immigration will stamp a separate piece of paper but even if they do it will be very easy to see that you have come via Israel from your entry stamp into the next country. So if you cross into Jordan at Jordan River or Eilat it will be obvious you have come from Israel. Same if you enter Egypt at Taba.
The problem is exacerbated if you have a car. Firstly Israeli customs will record it in your passport (no separate piece of paper option here) and the hebrew text will stand out a mile. Secondly your carnet (which you will need to enter Jordan or Isreal) will clearly show your point of entry.
They know exactly what they are looking for so it would be something of a miracle if it were overlooked.
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