Just like poker, it is not usually a good idea to try to draw the one card that will complete an inside straight. Therefore, if you notice a late discard of a high card, the player has probably switched strategies and is close to gin or knocking. Good players will tend to discard high cards early in the game. If you are playing a weak player, avoid discarding cards that are equal to the ranks, or are suited consecutively to the cards he picks up. Strong players will never draw from the discard pile unless it completes a meld, but weaker players will.
His discards, and more importantly, what he takes, are reliable indicators of not just which melds he is going for, but how close he is to going out. You can learn a lot by watching how your opponent interacts with the discard pile. In the long run, you can often outscore your opponent by knocking early and often, even if you get caught out from time to time. Remember, most people play with house rules which award 25 bonus points for making a gin, but only 10 or 20 bonus points for an undercut.
That is why it is usually a good idea to be the first one to knock, especially if less than 15 cards are remaining in the draw pile. Knocking to end a hand is much more likely. Few hands end with a player completing all his melds.