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.

There are instances on AD that Brigade SSI are worn (173rd, 196th, etc.) but I have never seen an SSI for any battalion (that would be DUI) The guidance would come from your HQ unit, both AD and USAR.
For you, ARAC would be the guiding command. They either say you must wear ARAC or they say you wear 244th. 670-1 tells you where SSI are worn. It has never said what SSI is worn.

I was in the 3rd Sig Bde when I went to Iraq in 2004. We wore the patch on our uniforms and it was the patch we were authorized to wear on our right shoulders.