1986 Burger King Panel
 

I can't seem to open one of the Burger King Panels without leaving part of
the panel behind. Any suggestions?

Steam them.

(literally, boil water, put the cards in a colander on top of the water, and see if steaming them for a few minutes allows you to separate the panel w/o leaving residue/glue behind).

I haven't done this personally -- but have heard a few accounts of such from folks who are big onto player panel grading on the PSA registry-

Burger King Panel
 

Thank you, thank you :)