The Rushmore gas headlamps on a 1910 Locomobile and the shaking grate acetylene generator that fuels them are seen on the recent New England Brass and Gas tour. Ad copy below from Rushmore, shows how these lamps and the generator operate. The Old Motor photos.
The illustration below demonstrates how the burner in the lamp and the reflector send the bright flame from the gas out of the lamp.
The advertising piece below shows how the acetelene gas generator works. Small pieces of carbide rock are placed in the basket. The water dripping on it from above creates the gas which is piped to the lamps and burners. Carl Fischer later perfected the acetylene tank (Prestolite), with which all you had to do was turn the valve on to let the pressurized gas go to the lamps. The generators had a considerable amount of maintenance and planning involved with them.