Thanks for all the feedback. It's really helpful.
Sorry I wasn't more precise in my explanations of the pictures that I took. I saw two birds flitting around together. They disappeared into the underbrush, and then an individual came out from the direction they'd disappeared and landed for just long enough to get picture number 1 (taken at 2:49 PM). It then went back into the underbrush and out of my sight. An individual emerged a few seconds later and landed long enough for me to take pictures 2, 3, and 4 (all of the same bird, taken at 2:50 PM) before going back into the underbrush out of my sight. I walked back and forth along the trail for a few more minutes before the appearance of the individual in picture 5 (taken at 3:05 PM). They all disappeared after that.
Since all the birds disappeared from my sight between the sighting of the original two birds and picture 1, picture 1 and 2/3/4, and also between pictures 2/3/4 and 5, it's unfortunately impossible to tell if any of the ones I saw flitting around at various times were the same ones I photographed.
Picture 1 really does look like a Red-flanked Bluetail, which, if that's the case, must have been flocking with the others. Wish I could have gotten a better shot of it before it disappeared.
After seeing a mention in a reply to my post that the individuals in my pictures 2-5 might be Taiga Flycatchers, I found a discussion about the Red-breasted (Ficedula parva) and Taiga/Red-throated (F. albicilla) Flycatchers at
http://www.birdskorea.org/Birds/Identification/ID_Notes/BK-ID-Albicilla.shtml. But I couldn't glean anything definitive from it. Someone else might be able to. The Red-breasted (F. parva) is the only one listed in the Field Guide to the Birds of Korea, but it was published in 2000. A lot has changed since then.
Anyway, thanks again for all the feedback.
As an aside, on the same outing, in the midst of a group of the most commonly seen type of Long-tailed Tit in S. Korea, the Aegithalos caudatus magnus, I got a nice view of an individual not so commonly seen in these parts: the "White-headed" type, the A.c. caudatus according to the Field Guide to the Birds of Korea. That was really nice.