It was recommended to me that I work the lining thumb before the rest of the mitten rather than after, and I can see the reason in it - it would be really fiddly trying to pick up stitches with only a toddler-sized thumb-width worth of room to maneuver in.
The needles I'm using are too long for this tiny thumb, though, so the process is still very fiddly, and sometimes it feels like I'm trying to juggle a pincushion.
I'm not really sure that I'm doing this right, to be honest, but I forge ahead nonetheless. After finishing the last gusset increase row, I worked up to the eight gusset stitches, then used a new needle to knit those eight stitches, and another new needle to cast on four more stitches. Finally I took a third needle and joined the (20) thumb stitches in the round, and worked one round plain. On the next round, I knit to the last stitch, and then knit it together with the first stitch of the next round. In that next round, I decreased twice, and then once more in the following round, in rather random order, but the end result was 16 stitches. I knit 10 rounds, then k2tog around twice until 4 stitches remained, cut the yarn, drew through the remaining stitches twice, and wove in the tail.