Can I tap a creature in response to it being tapped?
You can't respond to &quot;being tapped&quot;; you can only respond to spells being cast and abilities being activated or triggered.
And that's what you have here. Your opponent activated Dromoka Dunecaster's ability, after which you both get a chance to cast instants and activate abilities in response (i.e. before it resolves).
You are free to activate Humble Defector's ability at this time[1][2]. Having been placed on the stack last, it will resolve first. When it resolves, it will have you draw two cards and then give your opponent control of Humble Defector.
When Dromoka Dunecaster's ability then resolves, it does nothing[CR 609.3] since a permanent that's tapped can't be tapped[CR 701.17a].


If it's your turn, due to the limitation imposed by the ability.

Technically, your opponent gets first dibs since it's their ability to which you are responding[CR 601.2h]. That said, in a tournament setting, it's assumed that a player passes when they get priority in response to casting an spell or placing an ability on the stack unless they explicitly retain priority.




601.2h Once the steps described in 601.2a–g are completed, the spell becomes cast. Any abilities that trigger when a spell is cast or put onto the stack trigger at this time. If the spell’s controller had priority before casting it, he or she gets priority.
609.3. If an effect attempts to do something impossible, it does only as much as possible.
701.17a [...] Only untapped permanents can be tapped