05 century washer fluid

When I turn on the windshield washer fluid the wipers go on but the pump does not pump out any fluid. I gave the pump power directly and it works. someone suggested the wand but the switch for the washing turns on the wipers. anyway to trace where the wires branch off from that switch and split to the wipers and pump.
any other suggestions?

Does it pump out washer fluid when you wire it directly?

So you powered the pump and it works, ok. Is there power at the red wire at the connector for the pump? If yes, check the ground wire, if no you'll need to check for power from the switch out of the column, which it sounds like you are doing.