言うか？言わないか？どちらでしょうか？Why do 馬鹿を言うな and 馬鹿を言え have similar meanings?

Question

It seems to me 「馬鹿を言え」 and 「馬鹿を言うな」 are pretty much interchangeable. Corresponding expressions in politer form also exist, 「馬鹿を言いなさい」 「馬鹿を言いなさんな」 So what nuances of meaning do they each have? And what's the difference, if any?

Why do they have similar, if not completely overlapping, meanings when one tells the listener to stop and the other says the opposite? 馬鹿を言うな seems pretty straightforward as a command telling the other party to stop with the nonsense, but what about 馬鹿を言え? This phrase appears nothing but counterintuitive. When someone says 馬鹿を言え, what kind of response do they expect from the listener?

Answer 1

I'm not a linguist, but I think this expression has "if you could" implicitly. 「（言えるものなら）馬鹿を言え」"Tell me the nonsense (if you could)", which implies that the speaker believes the opponent should not tell.

Answer 2

The following are my guesses.

Possibility 1: There is the expression 'バカも休み休み言え' to mean don't keep saying stupid things. 'バカ言え' derived from this with omission and change of the particle. There are some extensions of 'バカ言え', like those in the comments. This might better explain why most other cases do not work in the same way (e.g. 'バカなことをしろ' does not mean 'バカなことするな').

Possibility 2: For some reason imperative is used to mean 'に違いない' in the similar way that English must has double meaning. So バカ言え/嘘つけ means '(お前は)バカなことを言っている/嘘をついているに違いない' = It must be that you are saying stupid things/lying.