Jim and I are taking different approaches to figuring out what is going on with your pump wiring. You can decide if you want to humor Jim or I or both of us with our requests.
I believe your left side Intermatic switch is broken and not going on, or your freeze protection switch is broken, or some combination of those two.
I suspect what is happening is when your booster pump turns on power is backfed through maybe the freeze protection device into the main pump and runs it.
You have many wires that disappear from view and so I can't figure out what wire connects to where.
Below is your electrical box. I marked wires A,B,C,D,1,2. I need you to tell me where the other end of each of those wires goes.
In addition there are a few wires coming out of the freeze protection device on the bottom left that I circled in green. You need to tell me where each of those wires goes to.
If you are going to touch anything in the electrical box for safety YOU MUST TRIP THE BREAKER IN YOUR MAIN ELECTRICAL PANEL THAT FEEDS THIS BOX!
Or clip the wire ties and pull out all the wires from behind the circuit breakers so a picture can clearly show where a wire starts and ends.
The central wires feeding power from the main panel to this panel are clear. And the wires feeding the main pump and booster pump are clear.
And current electrical codes require a GFCI Circuit Breaker for pool pumps. For safety you should replace your pump CB with a GFCI CB.
If this is more then you are comfortable with then you should get an electrician to look at your box.
