Did he down tools? Not saying you're wrong, just an honest question.
Personally, I don't think he was 100% putting it in at the end. Not sure I'd call it downing tools though. I think Mourinho said that what was happening was natural when a player knows he's leaving. It might not even be a conscious decision but if his performance level or focus drops slightly, he's shown up massively at this level. The one performance I most remember, and respect him for strangely, was away to Olympiacos. He was utter dogbrick for 75 mins. One of the worst performances I've seen in a Spurs shirt and he gave the ball away so much that the commentators were commenting on it. Think it was 23 misplaced passes or something. Yet, he continued to show for the ball and tried to get on it. I'd have hauled him off at half time personally but he actually did really well for the last 15 mins. Thought that showed a bit of character.
When I think "downing tools" I think someone who is deliberately not putting in effort to force a move. I didn't get that with Eriksen at the time although his performance levels dropped hugely and I guess there is a counter argument to what I've just written.