Here is the drawing how you can connect new float switch with relay to your timer:
I will also use this space to explain how this timer circuit works:
Outputs are taken from either NC (Normaly Closed) or NO (Normaly Open) terminals. Whatever signal (earth or power) you put on C (Common) terminal that signal, is passed on NC terminal. NO terminal is empty.
Now you have timer inputs. You cen either use earth (for that you must use T2 terminal) or power (for that you need to use T1 terminal). So when you put signal on timer, timer is alerted, but still did not started to count time. You need to release the signal from timer input in order for count to begin.
However as soon timer is alerted relay changed its position from NC to NO and now you have connection from C to NO, and will remain in that state until you drop signal from T terminal when count will start and when count ends, NO terminal will be empty and NC terminal will again pass signal from C terminal.
Now, signal from C terminal will remain on NO terminal as long as you hold signal on T terminal. When you release signal from T terminal countdown begins, but if you return signal to T terminal before countdown ends it will stop countdown and relay will remain in state where it passes signal from C to NO terminal.