The smear looks like it may be normal or just a little off. That means
it will be tough to find. If you take a pix of the chassis something
may come to mind.
The clock probably uses a big cap to hold time. Batteries can surprise
you. I had an old Zenith R472 series clock radio sitting for years. My
sis needed one so I cleaned it up & test ran it a few days. It sat a day or two
unplugged & when it came up the clock was right ! Not bad for a
40 yr old battery
73 Zeno
LFOD !