While sitting here with way too much time on my hands I found a table I had prepared for my mechanic to find out what's wrong with the fuel system.
the engine was running.
Pump left-----Pump right-----Caution light p/left-----Caution light p/right
off---------------- off--------------on--------------------on
off-----------------on--------------on--------------------off
on-----------------off--------------on--------------------on
on-----------------on--------------off--------------------off
from here we switch the pumps off
off-----------------on--------------off--------------------off
on-----------------off--------------off--------------------on

don't say it's impossible.

Good grief is right.....:bored:

Maybe check the diodes in the CWAP.

Correct me if I'm wrong, it's been 14 years since I ran out of fuel in a longranger, but don't the Fuel Flow switches control the caution lights with either boost pump on. If a flow switch is a bit tired or partially blocked, 1 pump might not have enough pressure to put a caution light out. With 2 pumps on, both lights go out. Also after having both lights out and then pulling the boost pump CB. The opposite light to what was on, may then come on depending on the resistance in each Flow Switch after running for a while.

If the pressure from one of the Jet pumps is also a bit down ie. partially blocked screens or jet pump. That might be enough to turn out a light inconsistently to either of the pumps being on. Hence the left & right caution lights could be off with the opposite Fuel pump on.

Ask your Engineer to check the operation of each of the Flow Switches as well as the Jet Pumps & Screens.
Hope this makes sense and is a possible explanation.

Yup........... My money's on the Flow Switches. Notorious problem area especially on earlier switches.

R...