You can have the 'Trapped in Amber' effect from the new fossil archaeology artifact while on a mount by doing the following:
1.Get where you want to be 'trapped' on your mount(while mounted).
2.Enter an instance using the LFG(or BG)
3.Use the 'Ancient Amber' while inside
4.Drop group(might be able to just port out with the LFG button, but I havent tried) and it will kick you out to your previous spot and state(mounted) while keeping the Trapped in Amber effect active.
WARNING: Do not use a spot high in the air for your mounted spot, as being trapped in amber will render your mount flightless.(And you will fall).