A lot has been said, but nothing has been actually answered haha. 4 hours is way more than enough to transfer between the two airports. To get to GMP you MUST enter Korea landside - pass immigration, collect your bags and enter Korea. Take the limousine bus to Gimpo Airport. The train is technically faster by distance between ICN T1 and GMP but when you add in the ten minute walk each way to the train platform, waiting for train etc- bus is better. The bus is right outside T1 Arrivals and will drop you off at GMP International Departures door. Can pay by card.

That expressway from ICN to GMP has no traffic as it exists only for ICN airport.

If IRROPS exists - they can handle it at ICN and perhaps even put you on ICN-NRT if you don't wanna wait for the next GMP-HND.

That being said - you can get to GMP and check in for your flight to HND with just 40 mins to spare (minimum check in time) and be TOTALLY OK. GMP is a TINY airport - no security wait, just five gates, VERY EASY. Even if you arrive 45 mins before - you'll be bored.

I recently arrived at GMP at 7:18 AM and check in closed 7:20 AM aka "busy morning departure times". No security wait. No immigration lines. We still sat around for like 15 minutes waiting for boarding to be called.