Below MCT, more than 24 hours. What do?
 

I'm planning a route with a loooooooong connection and I was hoping to go ICN-HKG-FRA.

TG629 ICN-HKG arrives @12:55
LH739 HKG-FRA departs @ 13:00

Obviously I can't connect in 5 minutes but I can't treat that as a connection because it exceeds 24 hours; it would count as a stopover.

Is there an obscure rule (such as the one where you are allowed to keep something a connection as long as what you are connecting on to is not a daily service) or do I just need to pick a later flight into HKG?

Stopover/connection/MCT rules vary slightly from airline to airline. Which airline are you actually planning to book the ticket with? Is it an award ticket or paid/revenue ticket?

Reward ticket on AC

I always understood it was next flight out....

Recall a case where NFO was 3 days!

Next flight out is normally the rule, but you'll likely need to call and book through an agent, of course. YMMV.

You just need to pick a later arrival into HKG as that rule only works when there is infrequent service available at a connection point and I'm quite sure that isn't the case between ICN & HKG.

Also your choice of trhead title isn't exactly correct as you aren't under MCT you are over your max. connect time.

MCT=Maximum connection time :P

Problem is that ICN-HKG goes out in bands of morning and evening. And on top of that of course are the OZ blackouts.

OP, I hope you realize that a TG+LH combination on this route will set you back about $450-$500 in real money in scamcharges on this route.

Didn't work in the end.

Full story:
Changing a MiniRTW and was ditching Korea entirely because of a requirement to be home sooner than I wanted to be. I was hoping to sneak into HK for a night. It never worked out and I ended up going NRT-MUC-FRA-YVR on ANA F and LH F. Now the mystery is how I was only charged an extra $34.10 (and $90) for that.