How do I keep the drop bead from swinging forward on my vampire bite necklace?

The fix for the swinging drop is usually to stop fighting the movement and let it pivot on purpose. What worked for me was hanging the drop from its own tiny wrapped loop on a short piece of wire, then attaching that loop through the space between the strands rather than crimping it tight against either one. Basically a little figure-eight link connecting both strands, with the drop hanging off the crossover point. Because the drop hangs from a loose pivot instead of being pinned flat against the wire, it can wiggle with your neck but gravity keeps it centered in the gap. Your crimped version looks stiff because you locked the bead at fixed points on two seperate wires, and any slack in one strand tilts it.

That figure-eight pivot idea matches what I landed on for mine, except I hung my drop from a single loop that slides along a softflex strand instead of being attached at both sides, and it settles dead center every time I put it on. For the twisting, I evened the strands out by moving one crimp a couple beads over so both lengths matched, then added a small two-hole separator bead right where they meet the clasp. The rotation pretty much stopped after that, and the drop stopped wandering too.

Been making two-strand chokers since before crimps were even a thing, when we strung everythign on silk with an attached needle and knotted between beads. If you go that route, the drape fixes itself, thread settles and the drop sort of nestles into the gap on its own. For the rotation, get a real multi-strand clasp, not two rings on one jump ring. The old cone ends or a clasp with separate soldered rings stop the strands from trading places. Also check your spacer placement, if the two strands only meet at the clasp they'll twist on you every time.

I had the same wandering drop on mine and it turned out the drop itself was just too light. Swapped the little teardrop for a slightly heavier garnet bead and it basically self-centers now, gravity does the work. Might be worth trying before you restring anything. On the clasp side, mine did the same twist untill I put a short length of chain on one strand and adjusted it every time I wore it. Not elegant but it stopped the strands from wrapping around each other. Do yours sit close together at the clasp or is there a gap? A gap makes the twisting way worse in my experiance.