'Fair share' -- if you have a 2.5-ton vehicle driving 12,000 miles per year on public roads, you should be paying the same overall amount in taxes and fees for road maintenance as any other 2.5-ton vehicle driven 12,000 miles per year on public roads; it doesn't matter whether it runs on gasoline, propane, hydrogen, electricity, methane clathrates, a hundred squirrels running in exercise wheels, or pure thoughts. A gasoline tax was a fair assessment against drivers when virtually all private automobiles ran on gasoline, were around the same weight, and got similar mileage. That's no longer the case. If one person has a car that gets 25mpg, and another a carefully-designed fuel efficient car that gets 50mph, and another an electric car that gets its energy from the power grid and doesn't burn gasoline, but all have cars that are roughly the same size and weight and are driven the same distance in a year, the first person pays twice the gas tax that the second one does, but receives no increased benefit for his taxes, and the third person, despite operating a vehicle that has the same physical impact on the road surface, pays no gas tax at all, reaping the benefit of the road maintenance paid for by the other two people's gas tax payments without contributing to the cost of that maintenance.
Here is an idea, why not simply tax Electric/hybrid vehicles a use tax based on miliage and leave the gas tax alone?
As has been pointed out repeatedly in the comments here, simply doing an odometer check can't tell how much of that mileage was driven inside Oregon's borders. But given the experience with the "your phone data is private unless you once, fifteen years ago, called someone whose brother's barber is a cousin five times removed to someone who, twenty years ago, was a known associate of someone we might, based on a pattern of legal but 'suspicious' activity, might be someone that we would conduct an investigation into in connection with an act of terrorism that they witnessed by happening to be looking the right way with a coin-fed scenic binocular at a national park, in which case we get FISA to rubberstamp our request, allowing us to grab every bit of data about every phone call you ever made or will make, even after we decide not to conduct the aforementioned investigation" attitude of the NSA and CIA, expecting people to believe "The GPS unit will only record your mileage as being inside or outside of Oregon, can't be used to track your driving habits, and we'll never give that data to anyone" is probably a lost cause.