I would say that since the ticking sound is coming from the abs motor assembly itself then this bulletin (common problem) that I found may apply to your problem. I have never ran accross it myself but this is a GM bulletin I found in the service manual for your car, it was the only one listed for abs. if you think this is the route to go then I hope it helps you
ABS Light On - DTC's 46 and 86 Set
(Perform Diagnostic Procedure, Replace Center ABS Motor Pinion)
1991-97 Buick Skylark 1992-97 Buick Regal 1994-97 Buick Century 1992-96 Chevrolet Beretta, Corsica, Lumina APV 1992-97 Chevrolet Cavalier, Lumina, 1993-97 Chevrolet Camaro 1995-97 Chevrolet Monte Carlo 1997 Chevrolet Malibu, Venture 1993-97 Geo Prizm 1995-97 Geo Metro 1996-97 Geo Tracker 1991 Oldsmobile Calais 1992-96 Oldsmobile Cutlass Ciera 1992-97 Oldsmobile Achieva, Cutlass Supreme, Silhouette 1997 Oldsmobile Cutlass 1998 Oldsmobile Intrigue 1991-97 Pontiac Grand Am 1992-94 Pontiac Sunbird 1992-97 Pontiac Grand Prix, Trans Sport 1993-97 Pontiac Firebird, Trans Am 1995-97 Pontiac Sunfire
Some owners may comment that the ABS light is on with Diagnostic Trouble Codes (DTC's) 46 and 86 set (rear ABS channel will not move) as current or history. (DTC's 46 and 86 will be displayed as C1246 and C1286 on 1997 and 1998 model year vehicles).
A condition exists where the ABS motor pack gear (pinion) will bind on the motor armature shaft causing the motor not to move when commanded by the EBCM. This condition is aggravated by light corrosion between the pinion and shaft. Therefore, it may occur more frequently when the weather is hot and humid.
Important: Other EBCM and ABS motor pack concerns can also cause this condition, but they are not as common as the above cause.
Follow the included procedure (Attachments 1 and 2) for diagnosis. This condition may correct itself before the owner is able to bring the vehicle in for service. Therefore, if DTC 46 is set in history, and is not currently setting, the included procedure will instruct you to replace the center ABS motor pinion. The new pinion has a Teflon insert which reduces friction between the pinion and motor armature shaft.
If the included procedure instructs you to replace the center ABS motor pinion, use P/N 18029776. Please note that the new pinion is a direct replacement part which requires no modifications to the motor shaft. Follow the pinion replacement procedure included with the new pinion. Complete motor pack replacement is not required