Hi,
The BECM, Converts a electrical resistance into a analog and digital output, the analog output is the fuel gauge dial. The digital output is for the range indicator. (this will however change depending on how you drive it and is calculated by lots of other factors) The resistance values you should be seeing are 270ohm's when empty, 19 ohm's when full. and when the system gets to 175 ohm's the low fuel warning light will come on. at this point you should have approx 9 litres of fuel left. If you can I would set up a multi meter and see what resistance values you are getting. then when it plays about see if the value changes. It sounds very much like a connection problem. You may also want to check the earth for the pump unit as well. If it helps the gauge signal wire is the green / black wire which goes to pin 10 on the BECM, the Earth for the fuel pump is in the engine bay by the main fuse box.
I think it will be one of those faults were you are going to have to check everything. i would start at the fuel pump end and work your way forward.
But back to your original question. yes mine does alter. I have fitted 3 fuel pump/sender units over the last year. due to other problems. They have all played about. Have you tried fueling yours to the top (i.e 100 litres) what does it do then. what happens if you run it right down low. does it still play about. once the fuel level drops below half a tank.