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It doesn't make sense to me that the live well pump would have to be one for the raw water wash down pump to operate.

First I would check the circuit breaker near the switch to see if it has tripped or the fuse if it has one. If that isn't the problem I would work my way from the switch to the battery and the pump to make sure no conductors are parted or have loose or oxidized connections.

Finally, if your raw water wash down system was not a factory installed option I would physically check to see if it has a dedicated pump. Many owners add raw water wash down systems to their boats that use the live well pump for the wash down. This is accomplished by adding plumbing to the existing live well pump discharge and sometimes a "Y" valve.