Should be clipped into base like you note.
I would just get a RULE (auto pump or float switch model) from Amazon and install it.
Unclip pump, unscrew base, clip wires as appropriate, install new base, connect wires, and mount pump.
The wiring can take some time if you have a float switch wired into the circuit. Tight quarters and all.
Simple job, maybe an hour working slowly.
1991 ProStar / 351W with 1:1 Velvet Drive