To add to the comments from jonk's answer, there is a problem in using the float switch to directly connect to the battery. When the water level approaches the switch set point, the switch will bounce indeterminately between on and off. This is a common problem when one has an on/off threshold for a slowly varying\$^1\$ analog signal, and can be addressed with hysteresis. This means that the on and off points are different, and the output will latch to on/off until the signal changes enough to reach the other set point.
In this system, the pump draws a fairly high amount of power, which you do not want pulsing on and off rapidly. It's usually best to have low power switches. Low power switches are usually cheaper, smaller, and there's often more choice.
A potential solution is shown in the schematic below. You can use a 4001 quad NOR IC, which will run directly from the 12 V supply you have (I haven't included decoupling etc) and as it's CMOS draws very little current. CMOS logic cannot drive much current (about 3 mA with a 12 V supply), so there's a small MOSFET to drive the red LED. The resistor values are fairly arbitrary.
simulate this circuit – Schematic created using CircuitLab
The main feature is the use an SR (set/reset) latch to hold the state of the float switch until actively reset using the other button; this provides the hysteresis. When the float switch pulls one input of NOR2 LOW, the output of NOR2 goes HIGH, and is then fed back to NOR1. NOR1's inputs are both now HIGH, and so it's output is LOW. The red LED will be on when the output of NOR2 is high (which is what you want). The system is now latched in this state until the opposite process with the Reset switch. The reset switch can either be manual, or you could (for example) have another float switch higher up in the tank so when the water reaches this point, the system will run again. Anything that will pull that input LOW in response to a higher water level is fine.
The other NOR gates generate the correct outputs given the system state: the pump is only on when the PIR output is HIGH, and the output from the latch is LOW.
\$^1\$ "Slowly changing" is relative to the speed of the switching element. A high speed comparator, for example, could switch in one nanosecond and so a slow signal in that application could be MHz in frequency. A mechanical switch may switch in milliseconds.