"That's very cool! The fact that his voice sounded familiar to you, even though you'd never heard it before, is something that I'm sure many trainers could relate to on an intuitive level; I think it's indicative of the numinosity of the bond between trainer and pokemon - but I digress!
With regards to whether or not telepathy needs a trigger... this may be a good time segue into my research.
To give an immediate answer to your question: no - telepathy shouldn't need a trigger, as pokemon abilities are almost always apparent from birth. But recently I've been entertaining the idea that there are actually two forms of telepathy: the first one being the intuitive form, imparted by the ability that we call 'telepathy'; and the second one being a latent form, residing in all psychic-type pokemon, that can be independently developed or perhaps 'triggered' by some sort of event. I too have a pokemon with telepathy who isn't 'supposed' to have it, per say - that pokemon being my Girafarig. But, unlike your Espeon, I can definitively say that my Girafarig has Inner Focus as well - one of its more conventional abilities. So it would seem to me that my Girafarig's telepathy is not, in fact, the product of a formal ability; rather, it was independently developed by the pokemon.
Now this raises many questions, namely: are these two forms of telepathy functionally identical? and if so, does it then follow that 'telepathy' as a formal ability merely refers to the state of being naturally talented at the use of this ability latent within all psychic-type pokemon?
Or, if these two forms of telepathy are in fact different, then how do they differ? and how do they interact within pokemon who may have both 'telepathy' as a formal ability, and independently developed telepathy? Perhaps Nana could provide some insight into this..."
Lucian talked himself into a deep think... but quickly snapped himself out of it.
"Anyway! I would love to meet your Espeon, and try to communicate with him! Actually..."
He reached into his pocket and retrieved a pokeball
"Why don't I send out my Girafarig as well? All four of us can try to communicate with each other!"
He sent out the long neck pokemon, and awaited Alex's response...