Vegemite in Busan?
Of course if you know anyone in Australia or The U.K you could get some shipped. It's available in a squeezy tube nowadays so it should cut down on the weight a bit.
Is it widely available in the States and Canada? I presume not since my Canadian friend is always asking me for Marmite when I go back home!
Am afraid you'll be out of luck. Have scoured all over Korea for the same stuff. I ended up getting a couple of jars sent over from NZ. Two jars cost $40 NZD to get here. Pretty valuable stuff. You mentioned Seoul, where in Seoul can you get it? I tried but couldn't find it.
If he's prepared to come to Ulsan sometime, will be happy to do some toast and vegemite to satisfy a fix.
The Asian grocers in Itaewon (up hooker hill, as one other poster accurately pointed out), had in tubes last time I was there.
To get there go to Itaewon and take exit 3 and walk straight. Take your first right turn, just after Dunkin Donuts and walk up the hill, it's on your left towards the top. Don't be put up by the 'Hooker Hill' part either. I think they sleep during the day, and the area is perfectly safe.
Here is a map. The blue arrow marks the spot
Here is a picture of it http://map.naver.com/?dlevel=13&lat=37.5335684&lng=126.9956061&query=7IS...
the main street is behind to your left.
Of course you might want to phone before going there. Phone number on sign says 02-793-0082, place is called 'Foreign Food Mart. Who knows they might deliver as well!