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Gut feel, if it's the original '87 transmission, it's likely a TK5, though there's a reasonable chance it's an FM145 or 146. The Ranger Station has a decent transmission identification page.
And, even if you did get either of those BII transmissions to bolt up to a those engines, those big engines would rip those little transmissions to shreds. Those trannys did ok behind the 2.9L; they are questionable for use behind a 4.0L; and I wouldn't even start to try them behind any V8.