Check the ECM if it has the number 1228253 this is what is wrong with it. Replace it with a delco reman. 16198264 ECM. Aftermarket ECM's give trouble and some are the old 1228253 #. As a former buick part person I have sold many of these. My 90 lesabre would be going about 35-40 and shut off and I would put the car in neutral and it starts right up again. The 1228253 ecm is trash and must be replaced.

I own a shop, and think this: The clicking noise you are hearing may be a relay that is going or gone bad. They make a clicking sound when the latch in them pulls in to activate power, or ground to a circuit. The way to resolve it is; you must find which one is making the clicking sound, but first do this; Make sure all battery cables are clean, making a good connection, and are tight. Also; check the ground strap from the engine to the firewall to make sure its getting a good ground. Sometimes it makes sense to purchase a spray can of electronic cleaner from the parts store, and remove all the relays one at a time, and give them a good cleaning. Pay close attention to the plugs on them, as they can sometimes short from corrosion, and cause this exact issue. This will more than likely fix the problem. You can't say a relay, or anything else is bad until you rule out a connection as being the problem.