Only one of the Immortals is the Drunkard and Drunken Fist Master, though I can't for the life of me remember which one off the top of my head. The other Immortals have completely different styles. And their relationship to the Trigams is common knowledge. It should even be on wikipedia, and as I take a moment to look. . . here you go: Symbolism
. I would of course recommend digging for a few other sources and cross referencing, but that looks about right as far as I can tell going off memory and first glance.
If you want to apply the Eight Immortal Symbolism to your martial arts then I would highly recommend giving some time to the study of Ba Ying Quan. It is a martial art that was specifically designed off the symbolism of the Eight Immortals, and works to achieve basic proficiency in (rather than complete mastery of) eight martial arts (including Bagua and Drunken Fist) which represent the eight energies of the eight trigram's and eight immortals. And eight directions and a bunch of other eight-ish things, if you get really philosophical with it.
Were I to begin studying martial arts from the eight immortal's perspective, I would definitely begin with studying the Trigram's and Ba Ying Quan, then develop a more unified system from there. Since Ba Ying Quan is really just eight martial arts thrown into one, and an arguably more "complete" style would be a more unified approach to exercising the essence of The Eight Immortal's in a martial way. A lot like Bagua invokes the Eight Trigram's a lot, but the invoking the Trigram's and invoking the Immortal's will ultimately lead to two very different experiences and styles. Because even though the Immortal's correspond to the Trigram's, they are ultimately "living" beings and not raw natural forces like the Trigram's are.