As was said, something is not right. Just because the old pump was working does not mean it was right either.
#32 is a 120V breaker. A 240V breaker takes two slots and has attached handles, like the 30 amp one in 26 & 28. You CAN wire a 240V circuit into two separate 120V breakers (which is what I suspect was done in your case) but it is not code, and is dangerous. One side can trip while the other remains hot. Two connected breakers ensure that when one leg trips, the entire circuit trips out.
So, be careful when doing your testing / investigation, things could still be hot.
What is with that ball of vinyl tape on the motor connections?
With the breaker on and the timer off, you should have 240V between terminals 1 and 3 on your timer.
The way I would start is by taking the cover off of your main panel and looking to see exactly what breakers / buss bars that circuit is connected to. That way I can make sure I deenergize it before working on it. However, if you are not familiar or comfortable working in your load center, please do not take the cover off.