Those safety clips go through the hole in the float valve (of course) and around the float tang the valve presses against. It helps hold the two together, and the purpose, I presume, is to ensure the valve opens the instant fuel level drops.
The bulb contacts are important, but another place to check is where the large wiring harness plug attaches to the light board. Those pins are just a press-fit connection to the light board traces and corrosion builds up at that point. Checking with an ohm meter can show thousands of ohms resistance when it should be close to zero.
Wanted: Dead, smashed, crashed or trashed gauges
BMW GAUGE REPAIRS - TACH*SPEEDO*CLOCK*VOLT METER *PODs & LIGHT BOARD*