It sounds like you have a bad power connection to the climate control, probably its ground. It's good enough for the relativly low current draw of the climate control but not enough for for the relatively high current draw of the pump. Double check your old pump, I'll bet it doesn't turn.
I heard the pump will come on when the engine is turned off and is hot to cool it down. Anybody know if a 190e does that?
5 speed '91 190E 2.6 320,000 mi. (new car, fast, smooth as silk six, couldn't find any more Peugeots)
5 speed '85 Peugeot 505 2.5l Turbo Diesel 266,000 mi. (old car, fast for a diesel, had 2 others)
5 speed '01 Jetta V6 (new wifes car, pretty quick)
5 speed '85 Peugeot 505 2.2l Turbo Gas 197,000 mi. (wifes car, faster, sadly gone just short of 200k )
5 speed '83 Yamaha 750 Maxim 14,000 mi. (fastest)
0 speed 4' x 8' 1800 lb Harbor Freight utility trailer (only as fast as what's pulling it)