Who would manufacture such a camera to be battery operated?
That would have to have been a huge battery to power such a huge camera.
And a huge tripod, too, with remote control arms, etc...
In fact, who was the manufacturer of all this equipment?
And who made a remote transmitter of that caliber that could relay over 238,000 miles to earth and back in 10 seconds?
Where did you get the three seconds of remote control delay, btw?
And where is this camera, now?
At that time, no one was using portable video cameras... they were still using 16mm film.
But that would have been impossible on the surface of the moon... to remote control a film camera... right?
Waaay too much in the way of electronics. It would have to be the a regular satellite, to transmit back to earth, right?
With the moon spinning and the earth spinning so fast, and the moon spinning around a spinning earth, which in turn is spinning around the sun... there is no way that you could transmit back to earth in less than 10 seconds using c. 1970 technology, right?
I Googled it. There are a bunch of them that are not all that large.
It seems it took a couple of tries with Apollo 15 and 16 to get it right. A better explanation is here:
https://io9.gizmodo.com/how-nasa-captured-this-iconic-footage-of-apollo-17-leav-1671650186