I'd like to create a question to store the current time.

Scenario is that I'd like a participant to see a short text question pre-populated with current time (not date, just time). They would just click to continue.

Later in my survey I'd repeat a short text question pre-populated with current time.

Figure this should be doable with JS -- just wondering if anyone can tell me how...

Hi, you can set up a short text question and set the deafult answer to : {date("H:i:s")} . This will show the current time when the question is displayed. No need for javascript here.
Alternatively, you could use a text display question using the above expression as (part of the) question text...

Or : an equation question type : value are saved in your DB and user can not update it.

Maybe add {if(empty(self),date("H:i:s"),self.NAOK)}