The ball is about 8mm dia if I recall, just had one in my hand 3 days ago, I can pull it out and measure if needed.
There are two different length switches, I would not expect you would have been supplied the short switch in error.

If you have a small shop magnet check up in the hole to see if the ball is there. Or measure the depth and see how close the the threaded length of the switch.

Cheers, Charlie
If It ain't broke, Modify it!
87 Montero turbo Converted back in Spring1989
95 Montero SR 3.8 DOHC Only one?
93 Pajero 3 door 6G75 Mivec with paddle shifted 5 speed
Then a Gen2 SR with full coil independent suspension.