Kitchener stitch - last stitch?

I used the kitchener stitch to sew the tip of my sock last night, and was a bit puzzled on what to do for the last 2 stitches… since it works on 2 pairs of stitches on the front and back needles, what do you do when you have only one stitch on each needle? I guess for the front needle just do as usual (insert the needle knitwise and then drop the stitch) but how about the one on the back needle? You go directly to the step where you insert the needle purlwise and then drop stitch? That’s what I did, but the stitch was a bit loose. I managed to fix it so it doesn’t show much, but is there another trick?

Here is the website I learned with. It’s very easy with clear instructions.

When I’m doing the last two stitches, I “pretend” that there is another stitch after them. Using my mantra from Amy’s video, I will “knit” the first {actually last} stitch, and slip it from my needle. In my head I’m thinking purl, since that is what I’d be doing to the next stitch if it were there. Then I “purl” the stitch on the other needle and slip it off. It sounds kind of complex, but it’s actually just doing it as usual, and using a mind trick to be able to finish it off properly, the same way I use it to start my kitchener.