It eliminates “te” like “Hij will op vakantie gaan”. Why?
It’s hij wil with one L, not hij will with two L’s.
Willen is a modal auxiliary verb. In simple terms, modals express possibility (kunnen), necessity (moeten), concession (mogen), desire (willen), probability (zullen). Modals don’t take te. The only exception is the negation of moeten, which is niet hoeven te.
Think of it like the English modal verb ‘will’ — you don’t say “He will to go” but rather “He will go” — except that willen doesn’t mean ‘will,’ it means ‘want.’
Hij wil op vakantie gaan = He wants to go on vacation
But you don’t need to say gaan at all because the infinitive gaan is replaced by the complement op vakantie. Unlike English or French, a native Dutch speaker will simply say:
Ik wil op vakantie = I want to go on vacation (holiday)
Ik moet naar de wc = I have to go to the toilet (bathroom; washroom; loo; WC; water closet, etc.)