Wouldst thou like or likest?

The phrase "wouldst thou like" seems more appropriate to me, for the following reason:

As far as I know, "thou wilt like" is correct, and "thou wilt likest" is not, because the verb "like" is infinitive, here, due to the presence of the auxiliary verb "will". Therefore, "thou wouldst like" is correct, for the same reason. I don't see why rearranging the phrase into interrogative form should change the conjugation of the verb "like", but English is strange, and that's why I ask: Would it be correct to assume that the proper conjugation of verbs for the phrase I'm looking for is "wouldst thou like"?

The reason likest sneaks into this conversation at all is that it can appear (correctly) as a standalone verb in a "thou" construction, such as

I see that thou likest me not.

or

How likest thou the play, Gertrude?

But once you bring a verbal auxiliary such as wouldst or wilt into the picture, the special marker of "thou" verb forms is fully established, and like can appear unadorned in its place. As John Lawler noted in a comment beneath the posted question two years ago, the form

Wouldst thou like [not likest] a pottle of sack?

is not structurally different from

Would he like [not likes] a pottle of sack?

In both case the ending that would attach to like if it were standing by itself (likest or likes) is rendered inappropriate by the presence of the auxiliary (wouldst or would).