Could it perhaps be the other way 'round, that a drop in voltage temporarily starves the bike of electricity, leading to interrupted fuel flow and missed sparks? The first Gen DL1000 is well known for having electric problems, like migrated magnets, burned stators, burned connectors, burned switches in the handlebar clusters and so forth.
Reason I'm asking is that the rotor is connected to the crankshaft so as long as the crankshaft keeps turning, the charging system should be producing electricity. At 3000 to 4000 RPM that voltage should be well above 13.2V or so. If during the hesitation the rear wheel doesn't lock up altogether I cannot explain the drop in voltage other than through a loose connection.
You are using an independent voltmeter, are you? Not the voltage meter on the dash (if any), 'cause that can be impacted by ECU issues.
The clicking sound could be a relay. Do you have the Eastern Beaver relay kit for your headlights, or another relay for the headlights installed? Other possibilities could be the turn signal or fuel pump relay, and the starter relay on the starter itself. An interrupted fuel pump relay could of course explain the hesitation. I desperately hope the clicking is not from the starter relay - but that would probably sound way different.
