I think the traditional meaning of "shibboleth" went beyond word or phrase, to include such things as images and objects, as well. The fish symbol, for example, was used as a shibboleth for early Christians and has been, er, resurrected as a shibbolethic bumper sticker in the last few decades.
I have always had the sense that it was a bit secretive, as well. A frat boy displays his Greek letters, which to my thinking are not a shibboleth. There are shibboleths for the fraternity, as well, and they are not made public.
I heard somewhere that the FISH WAS SECRETIVE
of sorts, a kind of "password". In Greek it has some
spelling like ICHTHYS (I am not sure: don't speak Greek).
And it spelled a sort of 'anagram" : one letter for each
word "Jesus Christ, Son of God, Savior" - each letter
of ICHTHYS being one word. I know the early
Christians did not use a cross or crucifix as we do, any
more than we would use a small 'electric chair' or
hangman's noose, or syringe : and hang it on our walls
or put it above an altar in a church.