Yes, the coil is specific to the system. No, it's not likely tp be the problem. Check the primary and secondary circuits with an ohmmeter- - - -the primary should have about 1/2-3/4 ohm resistance and the secondary should have about 2,000 ohms or a little more. The most likely failure item is the module, followed by the pickup coil. The pickup coil should generate about 1/2 volt AC during cranking when disconnected from the module. There is no practical way to test a module without factory-specific test equipment, which some independent parts stores might have on hand.
Jerry