Typically a patch panel would be grounded via its physical connection (screws) to a metal rack that would be part of a designed bonding and shielding system.
Here is a great article on all the ways the ground path gets from the cable shield to the building's system.
If you have a free-floating patch panel (eg mounted on piece of plywood) that comes with a ground strap, the answer to "where do I connect it?" lies in, "where did you design it to be connected?". This doesn't have to rise to world-class data center standards. Is there a water pipe nearby? Or an electrical box that you could strap to with a screw? That might be good enough, and probably is if you don't have anything more sophisticated in mind.
Should you use a commercial Earth Bonding Plug? I don't see any reason why you should or shouldn't. If there are local construction codes or if you are working in a commercial environment where other people will be maintaining your work, there may be reasons to do it one way or another.