How long should I wait between facelift after eyelid surgery?

There really is no reason to wait. In most cases, I do both the eyes and the facelift in the same operation. The advantage is one recovery. If you choose to spread the procedures apart, then waiting several weeks may be the best option. This will allow the tissues to settle and the majority of the swelling to resolve before the next surgery. Good Luck.

This is a good question.
Why are you separating the operations? Facial and eyelid rejuvenation surgeries are usually performed together, and you should be able to find an experienced board-certified facial plastic surgeon to help you in this regard.
You should consider doing the operations together since face lifting tends to increase the amount of lower lid skin which could be judiciously removed (lower eyelid skin-pinch) at the end of the face lift.
Best regards.