We call them Hand-Off-Auto switches. I've done them two basic ways, both require a contact for Auto and Hand.
First way is all PLC, no bypass function. Wire Auto and Hand as inputs to the PLC. Auto means the normal logic is in control. Hand means run the pump, now. No Auto and no Hand is Off. Safety interlocks active in both modes, process interlocks may be active in Auto only. Used to manually pump out tanks below low level interlocks etc. Just did a project like this with all the H-O-As on ASi, worked pretty nice.
Second way is having the Hand mode independant of the PLC. I'm seeing less of a demand for this, but it's still out there. Here the Hand contact is wired in parallel with the PLC output. In Hand it runs regardless of the state of the PLC. A second Hand contact may be wired into the PLC to report status on the screen. Auto works the same as the first way.
In the case of your project, you can have all 24vdc on the switch. Wire the Hand contact in parallel with the PLC output, it will pull in the same relay that the output does to control the 120vac pump.
Edit: I see I misread your PLC output. Still, it's a good point in favor of using 24vdc output cards with separate relays to keep your 120vac wiring separate.
On the subject of "do you have to wire the Hand contact as an input"... If you are going to indicate the position of the switch on the screen, then IMO YES. You could fudge this indication as Jimbo3123 suggests, but his way relies on motor running feedback which we may not have for a 120vac pump. In an industrial situation, motor running feedback is common. However, without feedback on the Hand position, there is no way to report a failure of a pump in Hand. The indication is flakey too because the Hand indication only works if the pump is running and not in Auto. If it's in Hand and not running, it says the switch is Off, which isn't helpful if the pump is tripped out.