I am having difficulty finding the mechanism by which folic acid reduces the risk of neural tube defects. I know that it does so, but what in particular actually occurs with folic acid deficiency to cause the neural tube defect? Is that completely unknown and merely a strong association, or is there a putative mechanism?
You are having difficulties finding the mechanism because it is as of yet unknown.
Now of course comes the hard part where I need to prove that statement. Often, it's just apparent by papers not saying anything about the mechanism, even though you'd expect then to include a brief section if it was known, for example Folic acid supplementation for pregnant women and those planning pregnancy: 2015 update or the various Cochrane reviews on the topic of how much folic acid supplementation is optimal, or the WHO and CDC documents on the topic
Here's a few relatively recent ones that state it outright:
The mechanism by which folic acid prevents structural anomalies in the fetus is not known, but may involve the regulation of homocysteine metabolism
as FA deficiency may be a risk factor for NTDs additional studies will be required to determine the mechanistic role of the FA pathway in the onset of neural tube defects
FA = Folic Acid, NTD = Neural Tube Defects
To date, animal studies have not provided sufficient information to establish the metabolic and/or genomic mechanism(s) underlying human folic acid responsiveness in NTDs.
There are some putative mechanisms to do with folic acids effects on the homocysteine metabolism and its effects on methylation. I can't really tell how well-established those are yet, but maybe this can be a starting point for you.