It is starting to look like the fault may be in the gauge itself or in the dash
cluster. But to narrow it down a little further there is another test you can
do with the multimeter.
This test is to check the wire leaving the dash cluster and traveling all the
way down to the fuel tank sender unit is ok (brown/green).
Before you start you'll need to know the resistance again at the two terminals
of the fuel tank sender you've just checked. If the tank is still full
it can be better to use up a bit of fuel to drop the level back to half full or
anywhere other than full.
As you've seen from your checks the sender reads about 4 ohms with a
full tank of juice and 56ish ohms with the tank near empty. For the next
test ideally you want the sender to be reading 15 ohms or more (so
anywhere from three quarters full to nearly empty.)
The reason for this is if the brown/green wire had been rubbing against the bodywork
somewhere along it's run and was now touching bare metal, then when you go to test
the resistance along this wire you will measure 0 ohms. As a full tank of fuel also reads
close to 0 ohms then you can never be sure if the wire is reaching the fuel tank sender ok
or shorting to earth along the way.
At least if the fuel level has dropped down a bit the sender should be reading 15 ohms or more,
and then if you check the brown/green wire and find 0 ohms you can now be sure theres a problem
with the wire.
Once you've got your ohm measurment at the tank sender pins
(for arguments sake we'll say 30ohms),reattach the connector plug to the
fuel tank sender and make sure it's nice and secure.
Your now going to check the other end of the brown/green wire up at the dash
where you should find the exact same reading (30ohms).
To find the brown/green wire up at the dash you'll need to get access to
the rear of the dash cluster. Once you've done this you'll see 2 connector
plugs plugging into the rear of the dash cluster, a white and a blue plug
(there may also be a yellow and green plug if your car has an on board computer
or cruise control).
The plug you are interested in is the white plug (C2) as it contains the
brown/green wire leaving the cluster and heading for the fuel tank sender.
You are looking to identify terminal number 4 of this plug.
The picture below should help identify it. Looking head on at the
connector it's 4 up from the bottom on the left hand side...........
Unfortunately the holes in the connector are too small for the probe of
your multimeter to fit in to, so, you'll need a small strand of wire or a paper
clip to push into this hole to make contact with the pin inside. (gently)
When you have the wire/clip in place, set your multimeter to the
200ohm setting again, touch one probe off the piece of wire sticking out of
pin 4 and touch the other probe off the battery earth terminal or a decent
earth point on the car (ignition barrel is usually a decent earth).
You should get exactly the same ohm reading as you got when testing
the two pin's back at the fuel tank sender (+ or - 1ohm).
If you do, the wire from the dash cluster to the tank sender unit is sound
and the next step would be to swap in a different fuel gauge to the cluster.
(If your working at the back of the dash cluster while lying the cluster forward
on top of the steering coloum shrouds, it can help to place a rag/cloth over the
shrouds first to stop the clear perspex at the front of the dash cluster picking up