Here is how I interpret the site's behaviour:

Instead of looking for the "checked" property of the checkbox, the site wants the "_LocationSelection" value defined.

The checkbox(es) are used to set/clear this.

If you find a way to modify the value of "_LocationSelection.sel" without messing with checkboxes, you can probably proceed (until you hit the next issue).

I looked for a way to use Mechanize to handle "onclick" for a checkbox, but could not find such a beast.

Good luck.