Have you checked the fluid level? Not engaging is a sign of low fluid level.

 

It took a while but I finally got around to verifying this.
JTIS says:
"8.2.1 GENERAL DESCRIPTION This section provides information relating to the Powertrain 4L80-E transmissions fitted to the 4,0 liter supercharged engine (4,0L SC) and to the 6,0 liter engine (6,0L).
..........
8.2.1.1 Gear Ranges
With the Performance Mode switch in the NORMAL position, the vehicle will pull away in second gear. However, if more than 75 per cent of throttle is applied when the vehicle speed is between zero and 13 km / h (8 mile / h), then first gear will be selected. From 13 to 61 km / h (8 to 38 mile / h) first gear is obtainable by 'kick-down'. In 'sport' mode the vehicle pulls away in first gear and the transmission operates fully in all four forward gears."

So, the gear selected in sport mode depends on your right foot.
Today I tried letting my XJR idle away from a dead stop with sport selected. While rolling slowly along with the engine idling (slightly high idle) I switched to Normal, and the 'box changed up. I switched back to sport and it changed down again. Conclusive I think that it selects 1st when in Sport mode and second when in Normal (unless you stamp on the throttle).
And yes, it whines a bit in 1st.

 

Thanks, looks like I'll be keeping my XJR6 in "Sport" mode more often, just for fun if nothing else

.

 

Mine started off in first gear regardless of which mode was selected, regardless of throttle opening. Due to the info in the service manual I experimented with this numerous times to conclusively verify.



I guess mine was a freak


Cheers
DD

 

Doug, do you remember whether the sport indicator came on in the instrument panel?
The sport/normal switch applies a ground to the trans control module in sport and is open in normal mode, so a shorted switch would render you permanently in sport mode, but this would also cause the sport indicator to be on.