what is the grammar form where 找 is used twice in the sentence 林先生找工作找了多长时间?

Question

I'm learning Chinese by studying Zhongwen Red (中文 Red).

I've come across the following sentence: 林先生找工作找了多长时间? This sentence is from http://www.zhongwenred.com/R67.html.

This webpage spaces out the words and translates it like the following:

林 先生 找 工作 找了 多长时间?

Lín xiānsheng zhǎo gōngzuò zhǎole duō cháng shíjiān?

For how long has Mr. Lin been looking for work?

I'm wondering what the grammatical construct 找 工作 找了 means. Is the general format verb1 object verb2 了?

I have a couple questions about this:

1. What are some examples of sentences in this same format?
2. In verb1 object verb2 了, do both verb1 and verb2 have to be the same verb? If not, could you give some example sentences where they are not the same verb?
3. Does this construct need to be followed some word like 多长时间?
4. Does this have any relation to reduplication of verbs?
5. Does this grammar form have any meaning without the 了 after verb2?

Answer 1

This sentence structure arises in a sentence with a verb which has both an object and a complement.

...a single verb cannot be followed by both an object and a complement...
_{Degree Complements with Objects, Chinese Grammar Wiki}

One workaround (there are others) is to structure the sentence so as to repeat the verb. Ordinarily it arises in examples using 得 instead of 了, such as in:

你洗碗洗得干净。 (You wash clean the dishes.)

The use of 了 in this context indicates how far the verb has proceeded thus far, so while the complement doesn't have to be exactly 多长时间, it's restricted in some ways.

你写字写了多久? (How long have you written characters for?)
你跑步跑了多远? (How far did you run?)

It's possible to write sentences using a structure where there are two distinct verbs, although it feels like a different grammar structure:

我在大学学了两年汉语。 (I studied Chinese for two years at university.)

It's not related to reduplication of verbs.

Answer 2

Though I don't believe it is necessary for the example sentence you gave, there are cases where you're required to repeat the verb. I'd just post this as a comment if I could but I think this image sums it up nicely:

https://resources.allsetlearning.com/chinese/grammar/degree_complement