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I came across the following exercise for JLPT N2:
親に本当のことを言おうか言うまいか＿
a わからない b ３日も考えている c 関係ない
The right answer is b, which makes sense. Though I wonder why a wouldn't also be a reasonable choice here. Does わからない sound weird in this context, or is it related to the tense of the verb.
It will be easier to find out if you divide the part 言おうか言うまいか.
You can divide it as 言おうか and 言うまいか.
You can omit 言うまいか because it's added just to make it clear that 言おうか is an embedded question.
Then put each word (a, b and c) after 言おうか to see if it makes sense.
Now you notice that only the option b makes sense.
a. 親に本当のことを言おうかわからない。 → NG
b. 親に本当のことを言おうか３日も考えている。 → OK
c. 親に本当のことを言おうか関係ない。 → NG
Why "a" doesn't make sense? Because if you want to put an embedded question before わからない, か should come after verbs in the informal form/i-adjectives (this case for example 言った方がいいか（どうか）分からない)
言おう is the 意向形（いこうけい）(volitional form) of 言う. 意向形 of a verb + か is used to express that the speaker is wondering whether or not he/she should do something, and it doesn't fit well with 分からない, but it does with 考えている or 迷っている.
From the few JLPT related pages I've skimmed, it seems that the「V（よ）うかVまいか」construction is most commonly followed by「考{かんが}える」or「迷{まよ}う」like in your exercise.
From Global Aichi's Japanese Sessions:
仲のいい友だちに会うだけなので化粧をしようかするまいか迷うなぁ。
I'm hesitating to put on makeup just for meeting a good friend.
Ｎ１を受けようか受けまいか考えている。（受けるまいか is also possible）
I'm thinking about taking the N1 exam.
体調が悪いので行こうか行くまいか迷っている。
I'm not feeling good, so I'm not sure if I should go.
This blog post on Goo by Mojimojimojisuke shows three examples, two of which use「迷う」but also one which doesn't:
A：夏休みに国へ帰りますか？
Are you going back to your country this summer break?
B: 夏休みに国へ帰ろうか帰るまいか、まだ決めていません。
I haven't yet decided whether I'll go back or not.
Your safest bet when using the「V（よ）うかVまいか」construction would be to follow it up with「考える」or「迷う」as per the examples. Likewise, if you see the construction in an exercise or exam, remember to check if either of those verbs is an option in the follow-up.
But if I had to speculate, you could probably follow up with any expression that indicates an active effort to make a decision or to resolve a situation. Both「考える to consider」and「迷う to be unable to decide」fit this description, as well as「決める to decide」in the last example. The expression「わからない I don't know」indicates that you're somehow undecided, but it's more of a passive remark rather than an active effort to settle something.
