最終入館 is the short form of 最終入館時刻。
Grammatically, 最終入館(時刻) is considered as a single noun, which is why you don’t have to say 最終の入館時刻(最終-noun, に-particle, 入館時刻-noun).
In English, there are a few cases that a noun works as an adjective.
Example; rabbit hatch / cat food / tennis racket
Similarly, 最終(noun) works like an adjective that qualifies 入館時刻(noun).
However, gramatically, we don’t consider 最終 as a single adjective. 最終入館(時刻) is seen as a single noun instead.
最終の入館 literally sounds like "entry of the last" and a bit awkward whereas 最終入館 is the same as "the last entry", which sounds pretty natural.
When you see a sign board which says " last entry : 8pm", doesn’t that make sense to you? (Although it should be written as "the last entry time : 8pm").
It’s like the same kind of thing in Japanese.
Those words are collocations, and there is no certain rule to see when to eliminate の, which connects two nouns.
In English, "chocolate bar” would never called "a bar of chocolate" even though there’s no grammatical explanation for it.
In Japanese, 最終入館 is one of the same cases.
-Examples of collocations that eliminate "の"
起床時刻{きしょうじこく} 、就寝時刻{しゅうしんじこく} (time to wake up/sleep)
友達関係 {ともだちかんけい} (relationships with friends)
勉強時間 {べんきょうじかん} (hours of study)
Not always, but 〜関係、〜時間 、〜期間、〜確率 are mostly the case that eliminates の.
最終入館
<-- The last entry time to a restaurant would be more like 最終入店 or 最終入店時間, no...? – Chocolate♦ Jul 19 '18 at 22:49