If modal "would" (habitual) admits a past and a present (I dare not say "tense") and other modals, both auxiliary ("will/would" #1) and aspectual (may/might, can/could, shall/should) admit the same, why then the two categories for "WILL": I. auxiliary modal and II. aspectual modal? Looking at the similarities (i.e., pastness) has brought us to a point where we should be asking, "What are the differences?", notably, "will/would" (category I). Shouldn't it be in category II?
"Modals are not marked for tense. What is historically the past tense mark (e.g. the –d or –t, could, would, might, should) no longer indicates past time: e.g. I may swim tomorrow, I might swim tomorrow, To indicate an earlier time, the auxiliary “have” is added. e.g. I may have done that yesterday. Some remainders of the historical past tense can be seen in what is referred to as back stepping in reported speech (e.g. She says she will come becomes She said she would come.) Today, the past tense form indicates tentativeness or politeness rather than past time."
Source:
www.clas.ufl.edu/users/rthompso/interactioncommands.html