I had this same problem on my '96 mistake, just wanted to say thanks to everyone that put in their input!
But while I was reading the threads no one followed up that I could fine, so wanted to kinda follow up

I had this problem for months, inspection due this month so finally decided I should take care of it

. It was diag'ed eariler by the dealer when it was in for something else, they told me the MFS shorted out / burned, so that and a relay needed to be replaced, wanted a bit over $300 to fix it.
I bought a used MFS from a JY for $65 but that still didnt work (thought it was the MFS, based on what I read here and what the dealer told me and you could see on one of the male connections on the MFS, it had burnt looking marks all around it) I dont remember who it was, but in one of these "brake light" threads someone posted a pic of the MFS with an arrow pointing to the wire that went into the connector. Well that got me thinking and I looked inside that connector (the smaller connector, there are 2 that hook to the MFS) and there were 4 female type connections, well 2 of them were to far apart to make connection to the male connection on the MFS when it was plugged in. So I just took something small and pushed the female connections back together and after that I had all 3 brake lights working again