Cousin David: Your flash photography of David (my son) inspired me to do my own experiments. I used a hallway so I have left wall, right wall, and ceiling as reflector. The experiment spreadsheet is attached and the results are posted. I used evaluative metering for camera and ETTL for flash. I did not try manual exposure and flash setting.
The images are underexposed with the worst being the forward exposure. Left wall is best. This set up only works if there is a reflecting surface near by. That is to say the walls may not be close. Or the walls may not be white. And then the ceiling may be too high. Or your flash may be too weak to cast decent light the distance it needs to travel when you bounce. Here is an example of the light not being sufficient. Flashes are rated for how much light they can cast at a certain distance and f stop. The on camera flash is the weakest, but it is always there, while your flash may not be readily available. Most cameras have on camera flash now. This is definitely helpful as you see from Susan’s images which almost exclusively use fill flash.