“In time of war”?? Define, please. Are there combat troop movements on or near domestic soil? I don’t see any.
WWII was at least a war, and a total one at that. Ration books. Scrap metal drives. The problem is, if we’re at war now, then we were at war continuously from 1941 to 1991, and then again from 2001 through who knows when. (What does ‘done’ look like?) And even then, conservatives would say - have said - we were at war from 1993 on (since the first WTC bombing), but Clinton was too dumb to realize it. So we’ve been not at war for somewhere between 2 and 10 years out of the past 64.
So let’s define ‘war’, please, in a way so that it’s not a nearly perpetual state.
And you have said which sort of conservative you are.
No. We are not discussing the relative merits of policy right now, are we? Stationing units on an unwilling and unwelcoming college campus (like, say, Yale, which kicked ROTC off campus in 1969) would be terrible policy, which is why the military does not do it.
However, bad policy or no, it wouldn’t be unconstitutional in the least, and I fail to see how a court would find it so, given the broad power Congress has to raise and fund an army, and the fact that the Third Amendment clearly applies to a home only, and only then in peacetime or according to laws Congress might pass in a war.
Same with the Solomon Amendment. It may well be bad policy (I think it isn’t, but I will allow for differences of opinion here). However, it is clearly constitutional.
As to what kind of conservative I am, I generally am the sort who wouldn’t want to rejigger an otherwise clear amendment just because I have certain policy preferences. Such things can be handled quite well with ordinary legislation and regulation, as has historically been done with the military, its basing, and its recruitment.