I just tried a Google search on "Eveready 504 battery" and got a lot of hits. It appears the original is no longer made, but there are alkaline cell replacements.
Originally Posted by JohnRichard
I still have a Tilt-A-Mite, but it hasn't been used in decades and I would bet putting a $15 battery in it would show me the capacitor is shot! Perhaps there could be a way to replace the combination with a newer capacitor and some sort of off the shelf lithium battery(ies). Only having about 20 flashbulbs in my possession, I think it will just remain a souvenir of days gone by, albeit a handy and clever gadget in its day.