I think you need to get your mind out of the Part 61 gutter, with all its talk of “Dual Given,“ and join us up here in the world of Part 121!

When conducting any kind of OE, or when conducting Line Checks, you are not acting on the authority of you CFI cert, you are acting as an LCA under the authority granted in your authorization letter from the FAA in conjunction with your airline’s training or flight standards department. You are not Giving Dual in the sense of providing training in Aeronautical Experience as required for a Part 61 pilot certificate, you are conducting Part 121 required Initial Training, Differences Training, etc. to a pilot who has already possesses the appropriate certificates granted under Part 61. In a very real sense, you are not actually conducting training at all, but are facilitating the already certified pilot in gaining “operating experience, operating cycles, and the line operating flight time for consolidation of knowledge and skills” required by FAR 121.434.

Long story short (and this is most definitely my own method): I have never logged any time as a required crewmember when acting as LCA as Dual Given. I created a separate column titled “As LCA” for my own records and listed only Flight Time (i.e. when sitting in the left or right seat) in that column. That same time was logged as either PIC or SIC, depending on how I was listed on the Flight Release. Line checks conducted from the jumpseat are not flight time, and so are not logged at all. In this interpretation, Dual Given only applies to Aeronautical Experience required to satisfy the requirements of a Part 61 pilot rating.

YMMV.

EDIT: I was typing while Dash8widget was posting! Good to see we're on the same page!