I think, if the trans is original, that you just have a hard seal problem. 2-3 shift is the releasing of the intermediate band (front band) and the application of the rev/high clutch (in the drum that the intermediate band runs on). If anything gets in the way of that clutch, then you get no third. Sticking piston, messed up VB, etc.

I'd not a "chemical fix" kind of guy, but you can try a can of Trans-X or Seafoam in the trans with fresh fluid and see if there is a change. Surprisingly, that stuff can free up stuck seals for a bit. If a change is noted, then internal trans work is indicated. If no change is noted, then possibly you have a VB issue. You can also pull the VB and do a air pressure test to see how the front clutch responds when cold.

Broader is a good source of C4 performance items and experience.

Ps - I've had decent luck with the B&M kits, less so with the Trans Go stuff. So go figure. After years of screwing with C4s, I've come to the conclusion that VB are like carbs - you get a good one, keep it. And if one gets to not working right it can give you a real rash.

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1967 Falcon 4 door 351C - Owner built, owner abused.
70 Mustang 351C / 06 Ranger, 04 SuperCrew parts hauler