The dictionary has it wrong, or at least incomplete. A wingover doesn't require an "almost stalled" condition at all. To further break this down, a wingover is more accurately considered an aerobatic maneuver and it's principal component is roll. A Hammerhead (an aerobatics term) is similar to a pure vertical reversal in ACM but the predominate motion is in yaw, not roll.
Variations of "wingovers" occur during ACM including such maneuvers as a high yo-yo, pitchback, or vertical reversal. Also, in Humbles film there are two versions of a wingover. The first is the Yak's initial move where he does a high yo-yo. If you forget Humble and just look at the Yak's flight path you can see him coming in flat, pulling up, overbanking into the turn, and then recovering. It's really only 90 deg of turn but essentially a wingover type maneuver. Also, a much better example of a pure wingover is at about 2+25 where both aircraft are extending in opposite directions. If you watch the film from Humble's position you can see the Yak straightlining away on the deck, and pull up with an overbank to the right. Turn "tracks" on and you can clearly see these as examples of wingovers in an ACM engagement and neither is near a stalled condition. That's not to say that it can't happen near stall, it certainly can, especially in a vertical reversal. I have to disagree with Humble in that I would characterize the majority of the maneuvers as oblique loops since they are, in reality, not separate maneuvers but part of both a vertical looping fight as well as rolling and vertical scissors. Although these maneuvers include components of wingovers, (primarily a nose up attitude and overbanking) these terms more correctly characterize the fight than does "wingover".
So, that brings us to the OP's original question, "when is the "proper" time to use a wing-over?" There are several times when a wingover is appropriate. The Yak's two maneuvers are good examples. The first (really a high yo-yo) keeps the Yak from overshooting the Corsair's turn radius, converts E to altitude, and creates a longer flight path to control closure and allow the Yak to convert his E to a better position. The Yak doesn't do this well though. The Corsair has already completed enough of a turn that it's easy for him to keep the Yak in front of his wingline. With the Yak's tremendous E advantage (500 mph compared to 300) he could have pulled a more agressive and sustained yo-yo into an almost pure vertical reversal that would have put him directly above the Corsair in which case he could have completely neutralized the Hog's turn rate/radius advantage. At this point the Yak would only have to roll in the vertical to put his lift vector on the Hog for a better shot opportunity than he had.
The second example at 2+25 is an outstanding example of a pure wingover and serves a completely different purpose than the yo-yo. In this case it's the "pitchback" portion of an extension/pitchback maneuver or tactic. Prior to the wingover, the Yak is on the deck and opening at about 250mph. He then pulls up and overbanks to the right completing his turn at just under 200mph with a small radius due to his nose high turn but finishes his maneuver nose low and accelerating. He hits the next merge with about 315mph, 65mph faster than his previous merge. What he's accomplished is to gain sufficient separation that he can redefine the fight with another merge (although things still don't work out for him). The wingover allows him to quickly get his nose turned around efficiently by using the vertical while he gains more E than he had at the previous merge. This type of maneuver is ideal for reversing on an enemy in trail, you just have to make sure that you have sufficient separation to complete the maneuver before the bandit is on you otherwise you'll just present him with a nice planform view of the airplane and a large target.
The vertical reversal is essentially the same animal but under different conditions and usually applies when you have an e or vertical position advantage on your enemy. Consider it a "wingover" where your initial flight path is vertical rather than horizontal. It's an outstanding method to reverse your direction of flight from up to down and differs from the others in that it can be very close to stall speed but it doesn't have to be. For instance, say you're ropeing someone with much less E. You could still be climbing at 150mph when your opponent stalls out below you. You should immediately do a reversal to head back down to catch him while he's vulnerable. If you continue up until you're near stall you're just giving him separation and time to recover and prepare to counter your next attack.