https://www.ecfr.gov/current/title-1...ection-121.436
It doesn’t have to be in the rule.
It says “under this part” which means the airline you are working for as a SIC needs to be certificated under 14 CFR Part 121.
In short, only time flown for a US based airline counts towards the 1000hr requirements.
You could have 1000’s of hours in N-reg aircraft but if the operator wasn’t certified under 135/121 it doesn’t count towards the requirements.
Now, what question is really on your mind?
https://www.pprune.org/rumours-news/654017-brit-pilots-working-usa.html#post11608187