...I can see how to do it using the map
I don't know why Kirk says PM has no function for this, but Set GPS Coordinates may work if you don't let the user interface confuse you
Make sure the contact sheet presents thumbnails in default sort order. Pick a first thumbnail to represent the start of image sequence running in sort order. Set the GPS coordinates for that one image. Select the same thumbnail plus any number of following thumbnails, you may skip some, but do not select thumbnails that sort prior to the one you set the coordinates on. Right click the first image in the sequence and make sure the location indicator is where you want it for the other selected images. You may now use Apply to All (selected) or Apply to Remaining. Remaining apparently means images following (in default sort order) the one you picked as a reference. Remaining does not mean images except the reference. Apply to All overwrites the reference, but it does not matter if you do not change the coordinates and want changes applied to remaning only.
And do not pay attention to the Hillsboro thing that may appear in the input field below the map. I never understood the rationale for the design of that part of the dialog. If PM knows the name of the marked location, that name could show in the input field. If PM does not know the name of the place, the Hillsboro name is worse than an empty field (for me, that is).