Watch oil is made from the porpoise' jaw, and I have not seen anything to equal it.

You may say why not oil the back pivots?
They do not need it as often as the front ones, because they are not so much exposed, and hence, they do not catch the dust which passes through the sash and through the key holes that causes the pivots to be gummy and gritty.

The front pivot holes wear largest first.
A few pennys' worth of oil will last many years.
It is necessary to occasionally oil the pulleys on the top of the case which the cord passes over.

If this is not done the hole becomes irregular, and a part of the power is lost to the clock.

Common oil will answer for them.