I use Superlube, which is silicone grease. If you don’t use that, use a traditional grease, even white lithium would be good. I find that most synthetic grease separates, and you end up with an oily mess.
Here’s what it looks like when the speedometer seal fails in the transmission, which is what they talk about in Smith’s instructions:
The speedometer takeoff in the transmission can be removed and resealed without dropping the transmission, and this should certainly be done if you have any trace of oil leakage around the angle drive. There are two seals, both are still available from the usuals.