The old pump doesn't only blow air, it's also sucking it. This old pump is connected to a "pneumatic diode" that separate the two different air flows.

The pneumatic switch selects which kind of air flow is connected to the single-acting air cylinder. Thus activating the cylinder by blowing or sucking.

Note that an Air-tank would be useless in such a circuit. See Old Pneumatics & Air Tanks.

It’s an easy to build piece but you have to sacrifice a present LEGO 48mm pump.
The 48mm pump has a one-way valve built-in at bottom of the piece. We will use it.

You need :
a : any plastic piece that will fit the split pump
b : the 48 mm pneumatic pump 
c : 4mm tube, LEGO ones (for example yellow tubes in Mindstorms kit) are good
d : a small 1x1 LEGO brick attached to a ring (space or Legoland piece)

Well this is time to split and pierce the pump. Watch the d piece fit the pierced pump.
Split the d piece to obtain a simple ring and cut LEGO tube c to 1,5 cm long.
Just assemble and glue the 4 new pieces.

Note that it won’ t work with 48mm pneumatic cylinder or old pump.
I haven’t tested it with small 32mm pump but I think it would work.