Turn the bike upside down, and put a single small drop of oil on all metal to metal contact points. Every one, even the threaded joints.

Leave the saddle mounted to the seatpost, as you will also be placing a drop of oil on all of those interfaces.

Then, try to wipe it all off, and some oil will have seeped into the interface.

Turn it right side up, and wipe it again.

Keep oil away from all leather parts, just put it on the metal parts.

Your squeek will be gone