Jumped light switch wiring
Alter the wiring to your left switch only slightly so it resembles this diagram:



Currently, your left switch has both the "power in" and "power to next switch" screwed to a common terminal. Add the "pig tail" and twist them together with a wire nut.

Now you can replace that switch with your timer where your "pigtail" is essentially your new power in. Your timer will likely need to be pigtailed to neutral as well.