Unfortunately, that link between vagotomy and reduced risk of PD hasn't been supported by subsequent studies. In fact, it wasn't really even supported by the initial study[1]: although the point estimates of the hazard ratios were below 1.0, the confidence intervals did not exclude 1.0 -- or stated differently, at p<0.05, the null hypothesis cannot be rejected.
Cool, interesting! Though I wouldn’t be surprised if there are such links, even if this one is not supported by further research. We know that gingivitis can lead to heart disease, so I wouldn’t be surprised to find that gut microbial imbalance could have other implications.
[1] https://onlinelibrary.wiley.com/doi/10.1002/ana.24448