Se sentir + verb is definitely correct French and here, the first form is better and more widely used although the second one is getting more popular in the last decades:

Like being plongé dans une recherche, vivre is something that has a duration so that one can better feel than vivant which is just a status.

This difference is probably more easy to understand when replacing vivre by other verbs.

Qui se sent mourir → who find death coming / who feel like to die.

Qui se sent mort → who feel like being dead.

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Qui se sent rougir → who feel a blush coming.

Qui se sent rouge → who feel being red.

Edit: Vivant has two meanings, the first and more common one is “alive” and I assumed that one in my previous statements. The second meaning is “full of life/dynamic” and in such case, both sentences would be more or less synonymous like qui se sent mourant or qui se sent rougissant would be in my examples.

Finally, note that you’d better use the third person in the subordinate clause because its subject refer to un type not the first je:

Je suis juste un type qui ne se sent vivre que lorsqu’il est plongé dans une recherche.

Le sens est sensiblement le même.

On pourrait dire comme autre exemple:

• je me sens chanceler;

• je me sens chancelant.

Sentir, comme tous les verbes de perception, sensation, peut être suivi d’une forme à l’indicatif :

• je le vois partir;

• je te sens venir;

• je m’entends délirer;

• je l’imagine rigoler;

• …