I am not 100% recommending the use of the original type of connector, it would depend on the circumstances. If it is in a domestic environment, it's not a good idea, because the connector when detached would not meet modern expectations of safety e.g. it's not touchproof for a child's finger. I mentioned it merely to add my personal viewpoint - I have many pieces of old electrical gear in original trim that are only accessible to electrically competent persons so it works for me.
Connecting the earth - I would look for a point that is in effective and permanent contact with the parts of the equipment likely to become faulty to the chassis, such as the motor & switch. Judging the best position to connect to, requires a certain amount of electrical experience. I would also test the continuity from that point to other relevant parts, to ensure that the earthing will be effective, before relying on it. The earth lead would also need a mechanical anchorage.
I was only guessing the type of connector required, it could also be the larger 'appliance connector' style mentioned earlier. If you can give diameter and spacing of pins this would become clearer.
Thanks for the extra pics - I never got involved with the BSR models so it wasn't familiar.