Thinking about this some more. I don't think the salt G. uses much power. You could run 4- #12 wires (H-H-N-G), from the 2-pole breaker, to the timer and come off one of the 240V lines for the generator and tie the neutral straight through to the SG. Sort of like a MWBC.
You would have to "pigtail" some of the wires, meaning join the needed wires, along with a short jumper(s) wire to reach the terminals. It would go like this.
The 2 hot wires, call them L1 and L2
Tie L1 to a jumper long enough to reach N/O1, and a jumper long enough to reach one of the timer terminals
[so L1 goes to timer terminal and N/O1]
Tie L2 to a jumper long enough to reach N/O2, and a jumper long enough to reach other timer terminal
[So L2 goes to timer and N/O2]
Wires to load (pump & SG), call them load 1 and load 2
You will need 2 load wires to the pump
You will need 1 load wire to the SG, along with a neutral
Use one of the wires as load 1 to the pump, use another wire (black) for the SG, and tie them to a jumper to reach the common 1
[so load 1 (pump) ties to wire from SG, and both go to common 1]
the other wire (Load 2) to the pump just connects to common 2
Tie the neutral from the panel to the neutral going to the SG
Both circuits will need ground wires, they all tie in with the ground ran from the panel.
Make sure you set the dip switch/voltage selector to 240V. The directions are in your timer but you didn't show the full thing.
Maybe this is clear as mud!