Hi,
I'd suggest 20W50 Valvoline or Castrol in the engine. My personal preference is either non-synthetic or semi-synthetic... I can't justify the extra cost of full synthetic, since the oil in my car is changed pretty frequently. I also don't like the fact that many full synthetic oils are heavy on detergents, especially the "extended mileage" type, and synthetic also tend to leak more, which is already enough of a problem with some TRs.
Under very cold conditions, 10W40 might be used instead (but, after all, most of our TRs are warm weather cars!).
In a non-overdrive gearbox, I'd suggest 85W95 or straight 90W GL4 gear oils (never, ever, never use GL5). The same can be used in a high mileage overdrive gearbox (either A- or J-type), but could prove to be little heavy, especially in A-type that run at higher pressure. 40W non-detergent (racing) motor oil might be a better choice for moderate to high mileage OD gearbox. A freshly rebuilt and "tight" OD gearbox might best be run on 30W non-detergent (racing) motor oil.
Rear diff uses 85W95 or 90W GL4 gear oil, too. If a limited slip diff is installed, a different oil might be recommended (check with the LSD manufacturer).
I'd not use synthetic in the gearbox or diff. Some TR owners who did have reported g'boxes started popping out of gear. The problem went away when they switched back to non-synthetic oils. (Note: Redline MTL might be okay. It's pretty good stuff from everything I've heard. Redline also offers friction modifiers, for use with LSDs. I just can't justify the price.)
I'd certainly never use synthetic oils in either type of overdrive gearbox. The OD is essentially an oil-bathed clutch and I've seen oil-bathed motorcycle clutches ruined by synthetic oils.
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