Generally, when you fly non-rev internationally (outside of Canada and Mexico), you'll need to head to the check-in gate. Even if you check-in online or through the app, you should head to the economy line and make yourself known to the check-in agents. Many stations will then tell you what time you should come back to the check-in counters, usually 60 or 90 minutes before the departure time (not boarding time!). They'll then clear folks in order and provide a boarding pass so that you can go through immigration and security.

It's hit or miss if the gate agents will let you go through security sooner if the flight is wide-open. In my experience, many East Asia stations (I've had this happen at HND, ICN, KIX, SIN) will stick to the T-90 or T-60 check-back period no matter what.

Beware: Even if they know you're coming, the gate agents will not wait for you. I once flew non-rev back in college (many, many years ago) from TLV and nearly missed the flight because the gate was at the very end, and I was chosen for extra security (5 on my passport sticker).