In E.T. when Elliott is at school and E.T. is alone at home with the dog, strange things start happening. When E.T. drinks beer, Elliott starts feeling dizzy. When E.T. watches a romantic scene on TV, Elliott kisses his classmate to whom he wasn't paying much attention earlier. What's the explanation for this sequence?
Director Steven Spielberg describes the bond between E.T and Eliot as a "double rescue".
Spielberg explains how he desired a friend like E.T. that he could share a special bond with after his parents divorce. He goes on to explain that Eliot has a need that E.T. can fulfill and E.T. has a need that Eliot can fulfill.
The explanation is that they share such a tight bond that they adhere to one another's physical and emotional state.
The interview with Steven Spielberg from AFI
Eliot and E.T. have a deep connection. Deeper than friendship. They have become one. They feel and think the same. E.T. wants to go home and his only chance is through Eliot. He therefore creates a special bond between them. Everything E.T. feels, Eliot does. It also shows to the audience the inseparable relationship between boy and alien.
The moment E.T. touched his glowing fingertip to the cut on Eliot's finger, which he got from mishandling the buzz-saw blade among the items collected to help E.T. build his S.O.S. beacon, the two were bonded physically & psychically.