For me it was not related with the order of getting those parts. Also, I did this quest after the latest update - don't know if this is important here.
Tarquin got stuck just after giving him the second part from Bloodmoon Isle. Right now, I also have the marker "Tarquin's Whereabouts" and he is not moving anywhere. There are no dialogue options.
I don't want to finish Act II without him, so I will wait for any news/hotfix...
