Next step I would try is to check the Anti-theft Alarm system for diagnostic codes. Read codes, erase all of them, repeat several of the actions which ought to trigger an alarm, and then go back and read codes once more. Report back what you find.
For this test, the diagnostic socket is #11, battery voltage is #16, and chassis ground is #1. I have attached a picture of X11/4 on your car. Refer to the general procedure which follows.
The code retrieval system generally works up to model-year 1996. After this time it is necessary to have an advanced scan tool to read most systems.
The diagnostics are wired to sockets of the car's main "diagnostic connector", X11/4. Early cars with continuous-fuel injection have 16 sockets, while later models have 38 sockets. The sockets are numbered, and each system has a single, dedicated socket for its diagnostics. For example: on a 1990 SL, socket #3 is for the fuel injection, #7 is for the roll bar controller, and #8 is the ignition.
Codes must be read one at a time. That is, you ask the system to issue a code, you read the code, you ask for another code, and so on. You ask a particular system for a code by electrically shorting its diagnostic socket to ground for 2 to 4 seconds. A second or two after the short is removed, a series of electrical pulses will appear at the socket. The number of pulses corresponds to the number of a code. The ignition must be switched-on for the code reading process.
Electrically, the voltage on a socket is normally high. Of course, with the short to ground in place it is forced low. Once the short is removed, the voltage momentarily returns high. The pulses which follow are transitions from high voltage to low voltage.
There are many ways to view the pulses for counting and reading codes. The simplest and recommended method is to connect an LED in series with a resistor between battery voltage and the diagnostic socket. I like to use an LED from Radio Shack (part 276-209) because it has the resistor built-in and costs less than $2. If you use a different LED and an external resistor, the value of the resistor ought to be between 470 and 2.2K ohms.
For convenience, the X11/4 connector has a socket wired to battery voltage and another wired to chassis ground. Also, you may wish to get some banana plugs for making connections.
Once you have read all of the codes, you may wish to go back and erase them. They are erased individually one at a time. To do this, read a code, wait a few seconds, and then short the diagnostic socket to ground for 6 to 8 seconds. It is my experience that when a code is erased, it is acknowledged by a single pulse on the diagnostic socket -- though this may not be the case for all systems.
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