I have always found triggering an encounter with a Thargoid Interceptor at a Barnacle site to be a dark art. I have had no luck in the past, they seem to be quite a rarity.
However there was a Barnacle site added recently as part of the Halloween event that works differently. I have been able to spawn multiple encounters with roughly a 50% chance with each relog.
In this video I explain where to go and how to do it.