Can the module keep the set selection of the parts finder (i.e. brand/model/year) when switching a category?
Yes, Product Parts Finder provides the opportunity to apply certain filtering parameters that will not be reset when a customer browses different categories.
To enable this functionality, navigate to Stores → Configuration → Amasty Extensions → Product Parts Finder → General and set the Apply Filter for Current Category Only option to No.
As a result, customers will be able to freely switch categories and keep the parts finder unchanged. To check the behavior on the frontend, set the required parts finder options and choose a category in the filters:
Then switch the category - the parts finder options remain the same: