The "chronometer" seen on the Jupiter 2 is actually a Spartus backwards clock which was sold as a novelty item in department stores.
During the opening scene after the robots warning about being in a gaseous area, the explosions occur before Dr. Smith swings his hammer.
The title appears to be a bit of a misnomer. There is certainly a cave but there are no wizards in sight.
Towards the middle of the show when Dr. Smith and the robot enter the cave, you can see a replica of the Jupiter II that the set director must have put there to simply try to pass it off as just another piece of machinery sitting on a red table just beneath the large gold colored eyeball.
The final position of the mummy that beckons Dr Smith into the cave is in a vertical standing stone coffin that has name NERO written down the side. The outer cave has Greco-Roman style columns and statues. There is also appears a Indian style statue in the left-side of the cave. Underneath the large eyed machine appears to be the model of the Jupiter 2.