Korean Air Skypass - KE lounge access

Flying in J on HKG-ICN-JFK route.
As KLM/AF Platinum and thus SkyTeam Elite Plus, do I have access to KE First Class Lounge at ICN? Or just Business Lounge?

I believe just the business lounge.

Confirm, just business. F is just for F travellers.

Here's another question:

I'm in F from HKG-ICN, and J from ICN-JFK. Will I be allowed into the ICN F lounge in this case? Is there even much of a difference?

Reality is very little difference. The F lounge is smaller and quieter, that's about it.

(Both have smoking rooms!)

Last month, I was flying on a DL J award ticket in KE, JFK-ICN, and I was allowed to use the F lounge in JFK because I was ST E+ via DL GM, though it was definitely nothing special. Was nice that it was less crowded though.