Trying to find photos of how I mount a three if these on the back of my touring. There is only one tiny bracket.
There are lots of accessory units that do just that, here's one of many.
I haven't added any extra electric lights to my 1915, but I can show you how I mounted the plate. My car is a roadster, but I'm told this is the bracket for a touring. I assume the one on your 1916 would be the same or similar.
It's common for the plate holes to be too far apart to match those in the bracket, so I used a piece of 1" flat stock with holes for the plate and other holes for the bracket.
Here's the same set-up on a 1923 touring.
I have converted my kerosene light (like the one in Steve's picture) to a tail / brake light without ruining the light or drilling any holes in it. I found a light socket that had a spring clip type mount that I was able to push up into the chimney snug enough to make a ground connection and ran the wires out the vent holes in the top of the chimney. I didn't even remove the wick holder / burner assembly. Wrap the wires in friction tape for an old look, or get some black shoe laces, the flat kind, and cut the ends off so that you have a cloth tube to run the wires through. Run the wires down the back of the lamp and across the bracket, and they are hardly b noticeable. You could just let the socket and bulb dangle if you soldered a ground wire onto it.
Some possible sockets are;
Napa LS6231 non-indexed, has a clip
Napa LS6230 non-indexed, no clip
Napa LS6458 indexed, has ground wire
1154 6volt indexed (pins are at different positions on each side)
1158 6volt non-indexed (pins same side to side)
1034 12volt indexed
1157 12volt indexed
I have also converted Model T electric tail lights to tail / brake by removing the single contact lead and replacing it with double contact leads and using an 1158 non-indexed bulb in the original socket. Just be sure to install the bulb so that the bright filament is on when the brakes are applied.
Leads are Napa LS6228, or LS6452