What is the Success Rate of Having a Skin Pinch?

Removal of skin below the eye, if unsupported, exerts force on the lower eyelid: downward force. However subtly, it can affect eye shape by rounding or by pulling down on the corners of the eye. In lax lower eyelids or if the pinch is more extensive, the deformity will be greater.
In our practice, we do not perform skin pinches without supporting the corner of the eye, usually with an ultrashort incision cheeklift (USIC). This also enables greater tightening than a skin pinch could without causing lower eyelid retraction.

This is a difficult problem to assess via photographs. An important portion of the examination is pinching the skin and assessing your lower eyelid tone. Based on what I can see from this photo, it is only my opinion that the laxity is too far down on the eyelid to be improved by a skin pinch.

Often times the skin is not "excessive" but the volume of the lower eyelid has diminished.  Skin Pinch or excision subcutaneously (same as the skin pinch) combined with orbital volume replacement will address the deflated lower lid.

Based on your photographs, I do not believe that a skin pinch is enough. It looks like you have moderate redundant skin on your lower lids. I think you would benefit from a subcutaneous belpharoplasty to elevate all the skin off of the muscle and pull it up (similar to tightening the sheets on your bed). If you do not elevate all the skin and just do the pinch, I think there will not be a significant improvement and it may lead to excess tension pulling on the lower lid. Since you have recently had a transconjunctival blepharoplasty and laser resurfacing, my advice would be to wait at least three months to allow all of the tissue to heal. Eye lid surgery is very complicated and repeated surgery can lead to big problems. Do no rush into anything. Good luck.

Dear Intears,
A skin pinch might help your lower eyelids or it might not. Dr. Moelleken is absolutely right to be concerned about lower eyelid support, particularly given how much excess skin you appear to have in your lower eyelid.
The amount of skin you need removed is actually much more than is classically addressed with a skin pinch. That is not to say it can't be done. However, this will directly couple the lower eyelid to your falling cheek, placing the weight of the cheek on the lower eyelid. This has the potential to alter the lower eyelid position even if the canthal tissue is supported with a canthoplasty, a more aggressive procedure than the canthopexy you had with your original surgery.
I am also struck by how hollow your under eye area is. This also matched the hollow upper eyelid sulcus evident in the upper eyelid. You are obviously not entirely sold on your surgeon's proposal or you would not be asking this question on the Realself website.
I have responded to two other questions you have posed here, and again, I strongly encourage you to seek other surgical opinions regarding your options.