Logging nginx rate-limited IPs into a specific file

Yes, you can do that, and a similar example is even in the nginx documentation.

The access_log directive also takes an optional if= parameter which evaluates variables given to it, and logs only if the result is not 0 or an empty string. Combined with the fact that you can have more than one access_log in a level, you can log differently based on your needs.

First, though, you will need a map to map the HTTP response status you are interested in to a variable. Remember that map must be outside the server block.

map $status $rate_limited {
    default 0;
    429     1;
}

Then in the relevant server block you will declare your access_log.

access_log /var/log/nginx/rate_limited.log combined if=$rate_limited;

Remember that any appearance of access_log in one level overrides all others from higher levels, so you will want to copy (or better, include) the access_log directives from higher levels that you also want to use.