What determines our SSI (unit patch) in the reserves?

To your first question, that is incorrect. There are MANY Brigades that have authorized SSIs. If you're in a unit under one of those Brigades (or assigned to the Brigade HQ), then you'll wear that Brigade's SSI.

AR 670-1 is pretty clear* (AR 670-1, Para 21-17d(9)).

Unless you fall into one of the exceptions of (a), (c) or (d), you'll wear the SSI of the unit you're assigned to. If that unit doesn't have an SSI, then the higher headquarters. If none have one as you go up the chain to USARC, then you'll wear the USARC patch.

Since the 224th has an authorized SSI, you wear that.
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* AR 670-1 - https://armypubs.army.mil/epubs/DR_pubs/DR_a/ARN30302-AR_670-1-000-WEB-1.pdf

I was with the 280th ROC, 7th ARCOM, Germany. When we deployed in 2003 we gave up the 7th ARCOM and became part of V Corps STB doing the G2/G3 Ops for V Corps Rear CP, so we wore the V Corps patch. I believe it depends on your activation orders. We were directly assigned to V Corps STB, thus the V Corps patch. Most all the 7th ARCOM units were in direct support of active duty units, so we wore the unit patch we were in direct support or assigned to.

I wore BDE patches on active duty. In 14th EN when under 555th I wore 555th patch.