Applying "change this face-up Attack Position card you control to face-up Defense Position" and "Special Summon that target in face-up Defense Position" are treated as being done at the same time.
The monster effect of "Wind-Up Rat" can only be activated once while the card itself is face-up in a Monster Zone. (Even if its activation or effect is negated, the effect cannot be activated a second time.)
When resolving the effect of "Wind-Up Rat", if "Wind-Up Rat" itself is no longer on the field, its effect of changing it from face-up Attack Position to face-up Defense Position cannot be applied, so the targeted "Wind-Up" monster cannot be Special Summoned from your Graveyard.
When resolving the effect of your "Wind-Up Rat", if your opponent has taken control of it (such as with the effect of "Enemy Controller"), you cannot apply the effect "change this face-up Attack Position card you control to face-up Defense Position", and the targeted “Wind-Up” monster in your Graveyard is not Special Summoned.
Mentions in Other Rulings
Weights & Zenmaisures: If "Weights & Zenmaisures" is activated by targeting a Level 4 "Wind-Up Soldier" and a Level 3 "Wind-Up Rat", if the Levels of the targeted "Wind-Up Soldier" and "Wind-Up Rat" are equal when resolving the effect of "Weights & Zenmaisures", your opponent will still choose 1 of those targets, but their Levels do not change. Furthermore, since their Levels were the same, regardless of which monster your opponent chooses, you cannot apply the effect of drawing 1 card.