Yes... A possible earth issue.
However by what you describe it sounds like the typical Alfa Romeo with a battery on its last legs. Believe me, they come up with some really wierd fluctuating faults when they are about to die
Go to any tyre and exhaust centre, they now offer free alternator and battery health checks that will find the cause quickly or at least, eliminate some possible issues....
Remember, you are under NO obligation to buy anything from them
They will perform a charging state test like Ronald has described above.
Then they will do what is called a "drop test" which will put the battery in a state of quick discharge to see how well the cells hold up... If it drops off the scale quickly than a new battery is the order of the day
If you fit one yourself , take the time to disconnect the negative cable and follow it to the inner wing... Remove the bolt and clean up the surfaces of the contacts.. apply a good dap of copper grease... do the same to the new terminals of the battery.
When you fit the positive terminal below the black fuse box to the battery, make sure that both thin rings top and bottom are on the post of the battery before nipping it up, not just the bottom ring.
Use a flat blade screw driver and a sight tap of a hammer to make sure the top ring is on
Chances are your electrical gremlins will disappear