Dummy noun, to add or not to add

Question

Most of the time (?) a following dummy noun is required when the speaker wants to put a 用言 where a 体言 is expected, as shown by the sentence below:

できないのをできないというのに、不思議があるもんか。

However, it seems that sometimes a 用言 on its own can function as a 体言, namely, with no dummy noun added, such as:

わかるまで待ってるがいい。

できそうもない幾何の問題を持って迫ったには冷や汗を流した。

So the question boils down to:

When a 用言 is used as a 体言, in what case is the addition of a dummy noun 1) required, 2) optional, 3) plainly wrong?

All three instances are from the novel Botchan.

Answer 1

The attributive form of a verb worked as a nominalized verb in archaic Japanese.

• How can （の）目指すは be grammatical?
• に越したことはない Wondering about the に

In particular, Verb + が + いい/よい is a highly old-fashioned and pompous way of making a request/command. It's mainly used as role language of pompous nobles today.

• <動詞の辞書形>　+　がよい ―　How is this allowed?
• Plain Verb followed by がよい

^{(待ってるがいい sounds a little unnatural today, though. 待ってる is a fairly colloquial contraction of 待っている, and がいい doesn't go well with such a colloquial expression. 待つがいい, 待っているがいい or 待っておるがよい would be more natural.)}

However, this type of nominalization works only in fixed idioms, proverbs and set phrases in modern Japanese. This sentence:

できそうもない幾何の問題を持って迫ったには冷や汗を流した

...is regarded simply as grammatically incorrect by today's standard. You simply need の after 迫った. Since this is from an old and famous novel, I imagine something like this may have been more tolerated in those days, but you should not do this in modern standard Japanese.