Wow- info jackpot! Hope your father enjoys the photo.
From the details of the suspension and wheels I'd say the ID as a Waverley Electric is hard to dispute, unless National copied little details like the pinstriping. The vintage is appropriate. I hadn't known about retrofitting hard-rubber wheels with pneumatic tires, but I guess when they became available, a less-jiggly ride was hard to pass up. Comparing the two I noticed the linkage that "steers" the headlight- the cars in the photos are a little different there, and the car in my ancestor's photo has no fenders- though those don't suggest a different model.
"Cox" was my ancestor's surname which is why I tacked it onto the filename.
Now I'm wondering- where do you plug in an electric car in 1905?
Dan Patterson