Sam, this really doesn't apply so very much to a Savage motorcycle as our headlights are ON any time the bike is running (which you do mention but never really deal with).  

Running a 12 volt relay off the existing hot wire to the bulb would not offer as much additional light as putting in say a Sylvania Siverstar bulb would offer.   It would likely cost as much or more than the extra bright Silverstar bulb, which would supply a good bit more light on low and really really burn up the road on high beams.

Plus, you don't really get into any specifics as to what relay to use or where to put it or how to actually wire it into the system.

Now, as a Rubber Side Down discussion thread, it is a good 'un to hash out -- which is better for you and best worth all the effort entailed?

1)   Put in a Sylvania Silverstar bulb

2)   Put in a CID bulb system (package kit)

3)   Put in the relay and use the stock OEM bulb

Sorry Oldfeller. I did a bad job explaining and the link my not have worked..  I know the light is always on.. That's why you would use the wire from the ignition switch to energize the relay. I forgot to put that in there.  

The relay set up has very little voltage drop.
I wasn't sure if the same thing can be done on a bike, guess not
I used 2 30amp relays my car with.
I'll put some more thought into it and see if I can have make more sense with the savage