After 1996, some Suzuki Sidekicks were equipped with a 1.8 L engine instead of the 1.6 L. These are called Suzuki "Sport" Sidekicks. As far as I know, the transmissions are the same for the 1.6 and 1.8 engines.
I used to have a 1998 Suzuki X-90 2WD with manual transmission and that model could be towed, too. [All X-90 have the 1.6L engine.] This vehicle should be equivalent to the 2-door Sidekick 1.6L version. For first generation Trackers and Sidekicks, there is no difference in the engine transmissions between the 2-dr and 4-dr models (except for the Sport model as described above). The early 8-valve 1.6L engine is not pertinent to this discussion.
As I recall, the Geo Tracker and Suzuki X-90 manuals all described how to tow the vehicle by tow truck and how to recreational tow. There was a lot of caution about towing automatic/2WD and any 4WD with auto-locking hubs. So one has to read carefully to make sure the prohibitions pertain to the vehicle as equipped.
I looked at the factory maintenance manual and for the 1997 Tracker, the 5 speed manual transmission is RPO MM5 (a Suzuki transmission) . The 3 speed automatic is RPO M65 (a Hydra-Matic 3L30), the 4 speed is RPO M41 (an Aisin 03-72LE). RPO=regular production options, this should be on label in glove box.
I would suggest you view the owner's manual of the Sidekick. When you read the recreational towing section, be sure that the prohibitions are not for the vehicle as equipped. Sorry, my Trackers and X-90 are being used by relatives now and I can't review the manuals(!).