Need help with Brake warning light diagnosis '86 5KCSTQ (long)

[Martin Pot]

Hi Guys. I have been plenty busy here keeping the 3 Audi's going, but here I
have one I am failing to solve the problem, and need your help. Here is as
much as I have observed.
I have been trying to figure out why my brake warning light keeps coming on.
First I had a leaky PS hose. I replaced both of them. Then my pump started
leaking, replaced it with one from Autozone with lifetime warranty. Flushed
the system and cleaned the canister and filter and did the lock to lock.
After I replaced it, I started having the annoying light and beep come on.
Then I replaced the hose to the bomb. Still beeping which made me to
conclude that the pump was weak. I took the pump back to Autozone and they
gladly replaced my pump.
All excited I put it on, but the light is still coming on. I have replaced
the bomb about 4 years ago.
I never had the light come on until I replaced the pump which still makes me
think that the trouble may be the pump.
Brakes are working fine, but steering seems heavier.
When I drive and brake hard, the light doesn't come on, but if I drive and
tap the brake pedal 5 times or so, very fast, only depressing the pedal no
more than a 1/2 inch,  the light will come on. If I drive downhill and let
the car cruise the light will come on with the least amount of braking. The
light will also come on when I am waiting to pull out of a parking lot, and
am applying some slight brake pressure.  If I run the AC at that time, it
will sometimes take 5 minutes before it goes out, eventhough my brakes feel
fine. If the car is all warmed up the light comes on more easily.  I am
still thinking that the problem is in the pump, because there seems to be a
relationship between RPM and light. When I take a trip on our curve two lane
highway, driving in the 50 and 65 Mhr range and plenty of braking for the
tight curves, there is no problem.
I am now to a point that I want to get a non Autozone pump or may be a new
bomb, but both items are expensive.
I really like to figure out what is causing the problem.
Thanks, Martin
'86 5KCSTQ
'91 2CTQ
'91 2CTQA