I put the finishing touches on my watch tonight including a case and strap:
The timer interrupt service routine is working properly and keeping perfectly accurate time.
The watch is being powered by half a 9v battery (AKA three 1.5v AAAA batteries). I estimate this will last it about a week.
It turns out the buttons and their diodes were designed to form a charlieplex button circuit. I have no idea why anyone would do this with only four buttons, but once I figured that out reading them made sense. The up and down arrows adjust the minutes or hours depending on if the index or enter key is being held down at the same time.
The project is completed for now but there is room for improvements. I could fit a PIN geiger counter in there and add a speaker for alarm clock type functionality. Driving a watch uses only a small power of the PIC18F2620’s processing power. I could have it synthesize speech to make a talking watch; among many other things.