I have always approached (and been taught) ikkyo as a martial exercise, rather than technique.
Rather than being a strong technique, static ikkyo practice teaches:
- Moving in and off the line of attack,
- Footwork and movement,
- Posture and breathing,
- And other very basic concepts (
hara, centeredness, maai, etc)
Nikyo (as well as Sankyo, Yonkyo, etc) then build on this foundation by adding effective pins and hand movements (holds, lock applications, etc).
Personally my Aikido differs slightly (only slightly) from that of JackBNimble in that in regular, static, practice, the Aikidoka should be focusing on the mechanics of the movement, making sure they are correctly applied. In ki no nagare practice, however, an Aikidoka should have the basic foundation already and should focus more on the opponent at hand, and less on the technique, developing such skills as zanshin, mushin, and maai.
And now I'm going to cheat and steal part of JackBNimble's answer, because I liked it so much I had to include it a second time:
Of course different instructors are going to have different styles,
and there is no right answer to say definitively which way is the most
correct way. The most correct way is the way that works best for you.