@CrisH Hey! You should be seeing these related grammar points at the bottom of every tab of the grammar point’s main page. Please let us know if you are not seeing the Related Grammar section at the bottom of the grammar pages. Cheers!
@ekhill Welcome to the community! Why don’t we take a look at all of the sentences on Bunpro that use a verb after そう(に・な) to see if we can better understand what is going on:
優しそうに犬を撫でた。
We use に here because it works as an adverb and modifies the verb (に can also modify adjectives and other adverbs).
Therefore it expresses the manner at which she pets the dog.
やさしそうに 犬を撫でた。[優さしい]
She pet the dog in a way that seemed affectionate.
な would modify the noun itself:
やさしそうな 犬を撫でた。[やさしい]
She pet the kind-looking dog.
彼はわかりやすそうに説明したが、まだ理解ができない。
Since 説明した is a verb, に modifies the explaining
わかりやすそうに説明した
Explained in a way that was easy to understand.
つまらなそうな話って聞きたく ない。
話 (はなし) is a noun and the part of the sentence that is being emphasized by そうな. If you were to place emphasis on the verb (聞きたくない) with そうに, the sentence would sound something like “I don’t want to uninterestingly/boringly listen to the conversation” which sounds a bit strange. You want to express “I don’t want to listen to a boring conversation,” so you would modify 話 with そうな
これが入りそうな箱ってある？
Similar to the above sentence, 箱 is a noun and you want to modify the object that you want to put something into (入る).
彼は真面目そうな顔をしているが、本当は遊び過ぎ。
If we were to use に here, it would sound like “He is diligenting a face” which sounds really strange. 
本当に起こりそうな夢を見た。
&
昨日またパーティーに行ったの？だから、眠そうな目をしているんだね。
Again, for both of these, we want to modify what we saw, not that we saw and what kind of thing we are doing and not what we are doing.
I hope this helps clear some things up. We try our best to give you hints that lead you in the right direction when you try one over the other. Let me know if you have any further questions. Cheers!
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