The aux pump is just water pump to get the coolant through the heatervalves. If one of them is stuck open (which is usually the default position if a valve fails) you'd always have heat on either the passenger or drivers side.
If such is not the case and the valves open and close randomly then it's probably electrical and I'd try to see if the valves are getting constant power (12V for closed and 0V for open).
The entire pump and valve assembly aren't hard to replace but new parts can be a little costly for its function. My valves were replaced at 50 euros by my mechanic. He used a functioning used one.
2008 audi A3 1.9tdi
(former 1991 520i LPG)