If my wife and I are stationed at the same duty station, but I am deployed, am I eligible for BAH?

YOu should be receiving BAH pay regardles of resdience with her or not. Your BAh is based on where you live, i.e zipcode. Your deployment should have nothing to do with it as well. This money is for home station housing. I would ask them to show you chapter and verse of the regualtion saying no, otherwise they should be paying you...and now IMHO it shoud be retroactive.

I'm not sure how the "you didn't live together prior to deployment" applies?

DTMO treats dual-military as separate individuals when it comes to BAH unless you have a dependent (your wife is not considered a 'dependent' since she is active duty military as well), so your wife's status should have no bearing on you. If you are not assigned government quarters at your PDS, then you're entitled (I previously wrote "have a lease" since that was floating around in my head, but that's for Reserve component who have been activated).

As such, a service member that is away from your permanent duty station (PDS) on temporary orders (TCS/TDY/TAD/etc) is entitled to receive BAH or government assigned quarters at their PDS (section 10.1.1 in Chapter 26 of DoD 7000.14-R* ... otherwise known as the "BAH Bible").

If your S1 is of no help and you don't have someone local you can elevate it to, you can elevate the question up to your MACOM RM (in your case, contact HQDA (likely) or TRADOC), or if you don't have one, directly up to DTMO* (use this process if you can't get any response from HQDA/TRADOC).
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* https://comptroller.defense.gov/Portals/45/documents/fmr/current/07a/07a_26.pdf
* DTMO submission link - https://www.defensetravel.dod.mil/Community/se/251137455B56AAAF08DB44E6356BDCB50E

It used to be, if you deployed, then whatever that you have is considered adequate quarters. Be it a hole in the ground, a GP large with 50 troops living in it or whatever.