1987 Testarossa Warning buzzer from dash help

That warning light and buzzer are associated with a temperature sensor (thermocouple) mounted in the exhaust system used to detect an overheating cat (or precat); however, a stock 1987 Euro Spec TR doesn't have cats nor precats? Has your TR been modified to add cats (like being a euro TR modified to be imported to the US)? Do you also have an added light for the 7-12 bank?

The light(s) and buzzer sounding at key "on" for a second or two is normal for such a system, and is the "self test" to confirm that the bulb(s) in the dash and the buzzer are working. Often it's the ECU running the light that fails and just wrongly turns on the light. If you have 2 lights (and two ECUs), the first thing to do is swap the ECUs and see if the other light now sometimes comes on, or not:

If the same warning light comes "on" = could be a real overtemp situation and needs more investigation.

If the other warning light comes "on" = most likely a flaky warning light ECU.

PS It can be helpful to add your location to your Profile. You don't need to be super-specific, but indicating at least which continent you are on would be a courtesy to others.

 

Then it isn't a "euro" TR -- it's a Swiss (CH) version TR.

Yes, that would be a condition for a "real" overheating situation (and, likewise, if you were getting the warning light 20 seconds after cold starting, that would be a sign that it is a false indication). However, the system should first provide a flashing warning light as it gets hot, and then go to a solid light when it gets really hot. Since you report it just goes from "off" directly to "on" solid = a sign of a flaky ECU. The slowdown warning light system operation is described in your 467/87 OM which only has text in Italian, French, and German. If you don't speak one of those languages, you can use a US TR OM which is very similar to your CH version TR (except the US TR has an air pump air injection system while your CH TR has a pumpless air injection system).

Not so much. What overheats a cat is unburned fuel entering a cat that is already at its rather high operating temperature -- so more an indication that that bank is set running rich, or has a problem to make it run rich (like the air injection system leaking air into the exhaust stream, and the O2 sensor signal fooling the injection ECU to wrongly add more fuel), or has a missing cylinder, or the cam timing not quite correct, etc.. Swap the warning light ECUs and see if it goes to the other warning light, or not. (And watch the self-test closely -- at every key "on", the self-test should work perfectly. If it doesn't = another sign for a flaky warning light ECU).

 

Yes, a Swiss version TR is much more like a US version TR than a "euro" version TR. ("euro" version is a term that we use here, but the correct, official F terminology is "standard" version TR.)

Or two dodgy warning light ECUs if your 7-12 self-test is not working, and your 1-6 warning light comes on randomly . These warning light ECUs have a long history here of going wacky -- I personally replaced 2 sets in ~20 years on my ex-TR.