Is the replacement light designed specifically for the Bobber Like the ones A&JCycles
Next, and Please don't take this the wrong way, but are you sure you hooked up the right wires to the new headlight? I included a pic of the original setup (from the Haynes Manual).
If everything is hooked up right, My first thought is a change in the circuit resistance is the issue. Your fuel gauge is basically a linear variable resistor, so a change in resistance in the circuit could make it do funky stuff
It maybe as Psychopasta said,, something is bad touching something it shouldn't be.. Are you getting any DTC codes? specifically P1619 or P1620? Either of those would indicate a short in the headlight circuit, Or, have you noticed anything else not doing what its suppose to?
Did you leave the plug for the side light intact? Try plugging the side light bulb back in first. If that doesn't fix it, try a quick wire tie together with the original light. If reconnecting either or both light(s) "fixes" it, and I'm making something of a leap here, Having that bulb out/disconnected is causing some sort of power deviation that is messing with the computer, and the result is the fuel gauge. It maybe that you need to "add" that resistance back into the circuit..
So if either of those fixes it. You need to determine the resistance of the bulb, (ie use an ohm meter between the bulb contacts) and try putting a resistor or two in place of the bulb, which fools the computer into thinking the bulb is functioning right. An example I know of is, if you replace a normal incandescent 194 bulb with a non resistance matched LED bulb, you need to add a 1/8th watt 1k ohm resistor to it to make things work right.
Alternatively, if it's the side light, you could add a halo ring (somebody had a thread about that recently) using those wires as the power, so the computer thinks everything is ducky and not do weird stuff....I had a quick look at the wiring diagram (also attached in PDF form: Part 1
) and don't see any physical connection between those circuit's, but that does not mean much once it hits the computer.
If none of this long winded diagnostic works, could be the sender itself took a spike of some sort which seems unlikely but you never know, in which case, sender time.
Or worst case (least likely) scenario, the computer took a hit
Hope something here helps, Good Luck!