"Push" often occurs as a technical term in medieval accounts of combats written in French. What seems to distinguish a "push" from other thrusts is that it's expected to include a lot of momentum transfer, and to knock the target back or down if everything goes right. This would be in contrast to a rapid pool-cue pop.
The combat at Vannes in 1381 seems like a promising starting point, since Froissart describes pushing attacks with the lance, and he agrees with Cabaret d'Orville, the other chronicler of the combat, that there were several knockdowns. Unfortunately, while Froissart and Cabaret agree on the broad outline of the combat, they disagree so thoroughly on the specifics of who was struck where that the core account of the combat that they both agree on tells us little about where exactly the combatants were trying to hit each other.
Here are some other accounts where the blow is specifically described as a push and where blows are said to hit.
Galiot de Baltasin and Phillipe de Ternant Fight on Foot with Lances, 1446
Edge of the bascinet, piercing it.
Galiot de Baltasin and Phillipe de Ternant Fight with Swords, 1446
On the bascinet, piercing it close to the earlier lance hit
Below the left shoulder, piercing and carrying away the gardebras
Top of the head. (Many great bascinets have perforations considerably higher than eye level. A thrust that lodged there could reasonably be described as hitting the top of the head).
Breaking the sword rondel
Piercing the gauntlet
Jacques de Lalaing and Jacques d'Avanchies Fight with Swords, 1450
De la Marche's Account
Between the left shoulder and the bevor of the armet, twice.
On the left flank
The pattern of hits described seems consistent with:
Aiming for the visor, and sometimes hitting points adjacent, and:
Aiming for gaps between plates, such as between the breastplate and armharness or at the inside of the elbow, and sometimes hitting points adjacent.