What plausible biological mechanism can explain how sticking tiny needs in your neck helps you get pregnant?

There is none, and yet Traditional Chinese "Medicine", also known as acupuncture but under a variety of terms such as folk medicine, traditional medicine, alternative medicine, complementary medicine...and then whatever new rebrand needs to be done when people stop paying for the old one. Mumbo-jumbo about Yin And Yang and Dao and Modalities and Mindfulness are fine, as long as you consult a real doctor. If you went to a legitimate specialist and got treatment but are convinced "music therapy" helped you get pregnant, okay, but don't pretend you should write a book about it.

This critter is not a fan of Traditional Chinese Medicine and wishes you'd stop killing him to drink his blood.

It's the same with acupuncture. Acupuncture works so poorly that even sham acupuncture performs as well for people as the 'real' placebo. That doesn't stop people from selling it to those with gullibility and a credit card.

The only limit on the efficacy of acupuncture is your budget. If you can afford to buy their placebo twice a week, great, but if not, once a week is still great.

If you read the New York Times because they endorse acupuncture and this nonsense, I know how you vote.

Acupuncture none times per week for your pregnancy issue would be great - for your bank balance. They are selling magic to rich white women. It only needs to work 29% of the time and if you are already a believer you will be convinced acupuncture is real. That is the definition of the placebo effect, and the hurdle acupuncture has never overcome in any clinical trial.

And never will.