Does modal "will" have mood or tense, and if so what is it?

Solution 1:

Historically, the English modals had tense, and mostly came in pairs of present/past: can/could, will/would, shall/should, may/might, dare/durst.

There are vestiges of this pairing still, so can, will, shall become could, would, should in past-tense reported speech. ("I will!" "He said he would!")

But all the originally past-tense forms also have independent uses, and in those uses it does not make sense to talk of any of them as having a tense.

In my view it does not make any sense to talk of mood in relation to them either. vaguer and less clear by saying "the volitional" instead of "modal will".