You should be able to type the first few characters to jump the that item in the list then press enter to select it.
Up/Down arrow keys will scroll through a list. Use typing as Todd suggests, then when you are floe to the desired item use arrow keys, then return/enter to select.
You could write a script to open it -- go to named layout object for some object on the popup -- then turn that script into a Custom Menu item and assign it a shortcut in the Custom Menu setup.
Be careful not to pick a shortcut which is standard for some other action in either FM or the OS.
I tested this in a new file by writing a script to go to a named object on the popup, and left it as #1 in the Scripts Menu, and the Cmd-1 shortcut then opens the popup from the keyboard.
If I understood well, you want the popup menu to open when you tab into the field, revealing the list of possible choices.
It won't work if you format the field as "pop-up menu", but it will work if you format it as "Drop-down list".
Once you are there, what Todd and keywords said applies.
Another way is to write a keyboard handler. The idea is to capture each keystroke and let a script decide what to do with it. i.e. filter the list in the popup (if you type a...z ) go to an item (if you press arrows), select the item when you hit enter.
Here is one example by Will Baker
That one is nice if the list isn't too long. It does a nice way of being able to do everything from the keyboard (filtering, selecting)
Ah, I see what you mean haha. The only option in my experience is either not use the built-in popover menu or do a little filemaker trick..
Duplicate the field, make one with a drop-down list the other with the popup.
Make the tab order so that it tabs into the drop-down field. Don't include the popup in the tab order at all.
Place both fields on top of each other, with the popup one on top and the drop-down in the back.
Now if you tab into the field you get the list which you can navigate with keyboard and if some one is a mouse user they can click on the popupmenu.
Kiss principle rulez