This has probably been discussed before but since I get the feeling of "I wish someone would have told me that." every time I get on this site I will pass this on.

RE: 65 Olds Cutlass

If your fuel gauge doesn't work before you start tearing too much apart check the continuity of the wire (brown on my car not TAN) that goes from the sending unit (and the units ground)to the front of the car via the "ribbon wire".
The wire connects with copper ribbon wire, through a hole in the backseat area. It feeds into the plug at that point. Mine came loose(not the whole plug, just the one brn wire) and reconnecting and securing it made the gauge work. I suspected this after doing a continuity test under the dash where the ribbon wire connects with the feed into the circuit board gauge cluster. On the Classiccare wiring diagram the ribbon connection isn't labeled well and the number of the connection points is not clear but it is there. Hope this helps. After working in the motorcycles and car most of the time electrical issues are bad grounds and bad connections. I always use di-electric grease when reconnecting these things.