Severe voltmeter needle oscillations

Voltmeters read a "difference of potential". You appear to have nothing between the leads of the volt meter across (in parallel) the fuse input and output so any time something draws power, it's going to change the difference of potential. When you hit the turn signal, that provides a path to ground, which causes the volt meter to see zero difference in potential. if you put one across the turn signal lamp, it would read nothing until the turn signal was turned on and a difference of potential was read across the filament (a resistor basically). When you measure across a bunch of parallel resistors, there will be a voltage drop, until/unless there exists a path to ground, which is what the turn signal is providing. yes it's going through the bulb and causing a difference of potential, but the way your meter is wired, you'll never see it.