Tom heeft zijn gordel niet mogen losmaken totdat het lampje uitging.

Because the speaker describes a past situation. Dutch uses the perfect tense with the auxiliary hebben (here heeft) plus infinitives to talk about past actions or permissions. When you combine a modal verb like mogen with another verb, both infinitives go to the end of the clause:

• heeft (auxiliary)
• mogen (modal infinitive)
• losmaken (main infinitive)

So Tom heeft zijn gordel niet mogen losmaken literally means “Tom has not been allowed to unfasten his belt,” referring to something that happened (or didn’t happen) in the past.

In Dutch, niet usually precedes the part of the sentence you want to negate:

• niet mogen = not being allowed
• niet losmaken = not unfastening (the act itself)

Putting niet before mogen clarifies that the permission was denied. If you said Tom heeft zijn gordel mogen niet losmaken, it would be ungrammatical. And if you wrote Tom heeft zijn gordel niet losgemaakt, you’d simply say “Tom did not unfasten his belt,” with no comment on permission.

totdat means “until,” and it’s a subordinating conjunction. In Dutch subordinate clauses you must move the finite verb to the end:

1. Conjunction: totdat
2. Subject: het lampje
3. All other elements, then the finite verb at the very end: uitging

Since the main clause is in the past perfect form, the subordinate clause also uses past: uitging (“went out/turned off”).

Both can refer to turning off a light, but there’s a subtle difference:

• uitgaan (“to go out”) is intransitive – the light goes out by itself or as a result of a system.
• uitdoen (“to switch off”) is transitive – you actively switch something off.

In contexts like car seatbelt lights or warning lamps, the light uitgaat (goes off) on its own when the belt sensor is satisfied, so uitgaan is more idiomatic.