I have an 03 SMT Spyder, and the reverse beep normally sounds when I put it in reverse.
However... and this is important, if it does NOT sound the beep ( sometimes erratic on mine) and I leave it in reverse for more than about 2 seconds, the engine will die, and I will need to play with the gear lever to get the green Nuetral light back to let the engine re-start.
I believe the erratic problem is with a sensor or relay, but I have no idea where ! I cleaned the 3 connections under the air box, as suggested by others.
The beep to me is a help, as without it, the engine would die and throw a P16 46 code.
The beeper is normal for 03 SMT spyders, and is a help in warning the driver of unusual transmission problems...... if it does not beep when in reverse.
Enjoy your ride.
Harryco.