Will a weak or almost dead battery cause flashers to stay on

Got everything installed in the bike. The brakes are fully rebuilt and now it looks like the steering bearings need to be replaced and while we are at it they are going to teach me how to do a fork rebuild. While they reinstalled the caliper and master cylinder, I wired the new signals and the speedo light. The turn signals don't flash... just stay on.
Was wondering (since my battery is really low) if it is just caused by the low battery or if I might have a darn bad relay.

 

With my old battery if the engine was not running they turn signals didn't flash. Brand new battery fully charged they flash with no problem. The old battery still works (I just moved it to my son's bike) it just drains faster then the new one..

 

Ya that sounds like a battery on the dying side. My battery is old and doesn't hold a full charge long as well. I need a new battery I think