As long as they want. They ask about convictions or tickets. Anybody that goes more than a few years back isn't getting good data and probably will ignore minor stuff many years ago. In fact most applications say ignore minor traffic violataions.
HOWEVER, falsify an application and you will get terminated as in FIRED. Now you have a real problem, because if if your next application aks why you are no longer there? and you don't lie again, you may be in deep kimchee.
If you have no other problems and you fit what they are looking for, a minor accident not your fault many years ago isn't going to make a difference. If you don't fit what they are looking for, then it doesn't really matter in that case either.
And BTW companies do check and companies will tell if you got fired for cause. The pendulum has swung back. As long as a company gives accurate information they are far less likely to be sued and lose than if they have derogatory information and don't provide it.