Stefnuljósið og ljósabúnaðurinn virka.

Those endings are the definite article attached to the noun, and the form changes depending on gender, number, and case.

• stefnuljós is a neuter noun, so the turn signal / the indicator becomes stefnuljósið
• ljósabúnaður is a masculine noun, so the lighting equipment becomes ljósabúnaðurinn

So both words are definite, but they take different article endings because they belong to different grammatical genders.

Yes. In ordinary Icelandic, the definite article is very often attached to the end of the noun.

So instead of a separate word like English the, Icelandic commonly has:

• stefnuljós = turn signal / indicator

• stefnuljósið = the turn signal / indicator

• ljósabúnaður = lighting equipment
• ljósabúnaðurinn = the lighting equipment

There are separate article forms such as hinn / hin / hið, but they are not the normal everyday choice in a sentence like this.

Because the subject is made of two things joined by og.

• Stefnuljósið = one thing
• ljósabúnaðurinn = another thing
• together: stefnuljósið og ljósabúnaðurinn = a plural subject

So the verb must be plural:

• Stefnuljósið virkar. = The turn signal works.
• Ljósabúnaðurinn virkar. = The lighting equipment works.
• Stefnuljósið og ljósabúnaðurinn virka. = The turn signal and the lighting equipment work.

That is normal for many Icelandic verbs ending in -a. The infinitive and the 3rd person plural present often have the same form.

Here the verb is virka = to work, to function

Present tense:

• ég virka
• þú virkar
• hann / hún / það virkar
• við virkum
• þið virkið
• þeir / þær / þau virka

So in this sentence, virka is not the infinitive. It is the 3rd person plural present tense, agreeing with the two-part subject.

They are in the nominative case because they are the subject of the sentence.

In Icelandic, subjects are normally nominative, and the verb agrees with them in number.

So here:

• stefnuljósið = nominative singular definite
• ljósabúnaðurinn = nominative singular definite

Even though both nouns are singular by themselves, together they form a plural subject, which is why the verb is plural.

The dictionary forms are:

• stefnuljós = turn signal / indicator
• ljósabúnaður = lighting equipment
• virka = to work, to function

The forms in the sentence are the definite versions of the nouns:

• stefnuljós → stefnuljósið
• ljósabúnaður → ljósabúnaðurinn

Because Icelandic normally writes compound nouns as one word.

So ljósabúnaður is a single compound noun, not a phrase split into separate words. The same is true for stefnuljós.

This is very common in Icelandic:

• one idea
• one compound noun
• usually written as one word

A useful rule is that the last part of the compound often determines the noun’s grammatical gender:

• ljós is neuter, so stefnuljós is neuter
• búnaður is masculine, so ljósabúnaður is masculine

In practical everyday use, stefnuljós usually means a turn signal or indicator, especially in a vehicle-related context.

Literally, the compound is built from elements related to direction/course and light, so the idea is a light used to show direction.

Depending on context, English translations may vary a little:

• turn signal
• indicator
• sometimes direction indicator

Because búnaður works like a collective or mass noun. It refers to equipment or a system as a whole, not necessarily to one single physical item.

That is similar to English equipment, which is also grammatically singular:

• The equipment works not normally
• The equipment work

So ljósabúnaðurinn is grammatically singular even if it includes multiple parts.

Yes to both.

If you leave off the article, the sentence becomes less specifically definite:

• Stefnuljósið og ljósabúnaðurinn virka. = the turn signal and the lighting equipment work
• Stefnuljós og ljósabúnaður virka. = turn signals / a turn signal and lighting equipment work, depending on context

You can also change the order of the two nouns:

• Ljósabúnaðurinn og stefnuljósið virka.

That still means the same thing. The main grammatical point is that the subject still has two parts, so the verb remains virka.