az-prospector, have you looked at the Fort's website?
The United States Army | Fort Huachuca, AZ
and here's a page within it that has some rules:
The United States Army | Fort Huachuca, AZ
I've looked around through the main webpage, and there's hundreds of potential links to wade through. The singular one above with some various rules, is not doubt not comprehensive, but ...... if you start with the main page, and navigate more, you might find base rules. Or probably something just to refer you to something else, like that all laws of the federal government apply (road speed limits, don't murder, steal, etc...), just incorporated by reference. I dunno. But at least there's a place to start to see if there's any "rules" that actually said "no metal detecting".
But I notice that your particular base has some "historic" (the word used on their website) originations. Ie.: indian war fort stuff. But it appears (if I'm reading the history section there), that that area is now under the nucleus of modern buildings and so forth. I did not read too in depth though. However, if you want to be "safe", you can always (just for common sense purposes) stay clear of sensitive historic monument zones. And it sounds like that's what you were going to do anyways, right?
If it were me, I'd race straight to the most historic zones possible, barring any signs or armed gaurds (because I prefer old coins

). But that's just me. But for sure, just as I have at various other bases around CA, hunt elsewhere. Afterall, you're legitimately allowed on base. And I see that they have recreation activities for the general public too there, to be on base.
If the PT fields haven't been hunted, those are often-time good for coins etc... And if you know of where the sand wrestle pits are, there are sometimes gold rings there, d/t the nature of wrestling in sand.
If someone were to .... for some reason ..... be out there in the boondocks, and take issue with your chosen activity ....... then ...... didn't you loose your wedding ring there last week?