Tunnels that are being used for civilian purposes (including smuggling civilian goods and supplies into Gaza) are not military objectives and cannot be directly targeted. As the occupying power, Israel may take reasonable and proportionate measures of control or security. This could include preventing unregulated entry and exit of goods, and ensuring that weapons and military equipment are not entering the territory.An occupying power has the ability to monitor and control the border of the territory being occupied, so it is reasonable to expect that power to be able to prevent unregulated entry of goods and to prevent weapons, by simply adding police to the border areas and enforcing the law.
But for Israel to do what Amnesty says it is allowed to do to prevent illegal smuggling under international law, Israel would have to invade Gaza and take over the entire border area with Egypt. It would have to methodically destroy hundreds of houses in Rafah that are hiding tunnels.
Would Amnesty approve Israel's invading Gaza in order to fulfill its obligations as "occupier"?
The definition of occupation is that the occupying power maintains "effective control." That means that it controls the police, the borders, and the government of the territory under occupation.
Effective control means that the borders can be properly policed. If they cannot be, then there is no effective control, and hence no occupation.
Amnesty (and the ICRC and HRW and UN) must jump through rhetorical hoops in order to pretend that Israel is occupying Gaza. But when you actually read how they try to square that with actual international law, you find that all of them are forced to come up with bizarre arguments that would be laughed out of court if anyone but Israel was involved.
If you want to see an even more egregious example of how the definition of occupation changes when Israel is involved, check out this document that the ICRC wrote in 2002, before Israel withdrew from Gaza, as a study guide to the laws of belligerent occupation:
Anything that the ICRC has written about Gaza being occupied by Israel after 2004 directly contradicts its own definition from 2002.