What is the ammeter showing?
A drop in voltage makes me suspect current is flowing. The questions are wheres it going, and where is it loosing power (resistance points).
Normally the voltage drop test is done with some equipment on or a 10 amps across a carbon pile resistor. In this case the only draws are the ECU and the coil, maybe the alternator field too but shouldn't be much.
So there shouldn't be any more than .1 V drop from battery to the run wire connection on the ballast. Check for drop at each accessible point along the way: solenoid relay, bulkhead in, bulkhead out,.
