Well, it's pretty simple actually.
If it does it with the car in neutral and parked, it's the flywheel forward.
If it does it while the car is in motion only, it's the trans backwards.
I've had the balancer shake, it's rather violent and destructive to the engine, even if it doesn't kill the engine immediately, a bad balanacer can start an engines demise.
The balancer should really fall under routine maintainance.
Make sure the one you have laying around is the correct balancer and try it out.
With a puller it should only take about 20 minutes.