Personally I think rectangular lamps in this location suit the lines of the rubber bumper cars well. For chrome bumper cars with them mounted in front of the grille, round lights matching the headlights would probably be preferable.
The additional lights are bolted vertically upwards into an L-shaped bracket. The bracket turns upwards in front of the valance and is held with one or two valance bolts. Whilst I have fitted new lamps to the brackets many years ago, the brackets were fitted by a PO and so I'm not certain if the holes and bolts were pre-existing for the valance or added by the PO.