An update of my research. I was worried that I didn't have enough detail of the maharaja of Charkkhari. And then, reviewing all my images one more time, I found a digital copy that I bought from the BL that features him pretty well.
Great shot of the Maharaja Sir Malkhan Singh, the parasol, the front panel of the howda and the mahout.
Watching this photo for quite some time I found out that there's a ladder hanging from the right side of the elephant. The white rope is holding it from both ends but, as the ladder is quite dark in the photo, it can hardly be seen. I don't have pictures of the elephant from the right so I would have never known. I went to the one of the films that was taken from the right and yes, the ladder is there