Our electric range/oven, no doubt original equipment when our house was
built in 1978, recently had its timer fail.

It's a GE range. The timer is a white third hand that is on the analog
clock on the range's control panel. You set the timer by pressing in on
a center knob and twisting, and then the timer sets from 60 minutes down
to zero.

It's a klunky device, but accurate enough, and most importantly, it
buzzes - LOUDLY - when done, and it remains buzzing until someone turns
it off.

However, a couple weeks ago, it stopped buzzing at all, resulting
already in a few burned or overdone dinners.

How easily can this timer/clock be replaced? There are a couple screws
along the top horizontal surface of the control panel, but I don't see
an easy and direct way to get just the timer/clock swapped out. And I
don't want to spend $120 on a service call just for a $5 clock.