The chart on this page also identifies it as an 89 S10 transmission.
http://www.britishv8.org/articles/borg-warner-t5-id-tags.htm
I wonder if it is a mish mash of parts or if this is an identification problem?
I wonder what the ratios in it really are? If it has that 4.03:1 1st gear, you might want a much higher rear end ratio, like 2.73 or 3.08.
4.03 1st x 3.73 rear = 15.03 final drive ratio in 1st. Insanely low. Granny gear.
4.03 x 2.73 =11.0 Still pretty steep but better.
2.37 2nd gear x 3.73 rear = 8.8.
You might just take off in 2nd, if the trans is geared the same as shown by those charts.
Assuming a 26" tire, a 0.76 overdrive gear and a 3.73 rear, you should turn 2931 RPM at 80. Not too bad.
Hopefully it's actually geared like a F body box.