And about your other question (do you actually want to do this), there is no fixed rule but here are some basic guidelines you can use:
Tambourine panned to the left, tambourine reverb panned to the right:
will contribute to a wide stereo image, sound more modern and will draw more of the listener's attention to this particular track
Tambourine panned to the left, tambourine reverb panned to the left
will contribute to a wide stereo image (provided that other elements of the mix offset this one on the other side), will add a vintage touch to the mix, but possibly sound unnatural
Tambourine panned to the left, tambourine reverb in stereo:
will blend more easily in the whole mix, sound natural and easy to balance
Experienced mixers feel free to amend/contribute, these are just my personal views on this.