Problems with starting and illuminating the instrument cluster.

Hi!
Testarossa 1991
I recently became the owner of a Testarossa. Recently the car was parked for quite a long time with the ignition on. Then when I tried to start it, I heard the sound of a large relay and everything went out. I charged the battery and the car started. However, the backlight of all indicators does not work. I thought it was fuse number 13, but no. I then parked it several times, turning it off and on again. Once when I turned the key it went off, but then it started again. Then after 3 days of stoppage everything started fine. Yesterday I left the ignition on for a while to check fuse 13 and again when I turned it on I could hear the sound of the large relay and the car was silent. I removed the battery and checked 12.6V. So rather good. But the battery was purchased with the car, so I will buy a new one.
Additionally, after inserting the key and turning on the ignition, there is a noise. I thought it was the air vent, but I turned it off and I can hear the fan behind the meter. You can also hear it from the trunk.
I know that I need to check the ground cables behind the battery, etc. The electrical installation in the car has not been modified yet, there is a relay at the starter and others.
I wonder if there is a ground somewhere? But what is that sound coming from the ignition?
What could be the reason for the counters not lighting up?
The car has a mileage of 54,000 km and had one owner, garaged since new, in beautiful condition!
Please help, I'm counting on you

 

And I actually didn't complete it, I didn't reach that place on the forum. I have no experience in such communities. I thought I was introducing myself but it could actually have been on another Ferrari forum, sorry for such a bad behavior. I completed the profile but did not find a place to enter the level of technical skills, only my profession. I'm not a mechanic, but I can do a lot on a car. I won't remove the engine myself, but, for example, I dismantled the front brake calipers myself and had them rebuilt by a specialist, and then I installed them myself and bled the air with my 11-year-old son Currently, I have nothing to do with airplanes, the nickname is historic.
I didn't hear where the sound of the large transmitter could be heard - the impact. This was a surprise to me and the car was in a single-seater garage with tiles on the walls, so the sound reflects off them. But maybe it was in the back.
Grounding is likely - from what I've read. However, I don't know if this may affect the backlighting of the indicators and the noise of the fan? I'll try to record today. But probably today after charging the battery it will be OK. After hearing the relay click once, no lights on the indicators work - as if the battery was completely discharged.
Where can I look for grounding? The battery and its cable, under the engine on the right and probably somewhere else?

 

Thank you.
I have a battery disconnect switch installed, but an additional one. My terminals are directly on the battery. Unless I missed something? Should this switch be somewhere other than under the battery cover? What are "cold cranking amps"?

 

Unfortunately, when I click on the YouTube window, an error appears and it does not work. Can you link again?

 

Thank you for all your suggestions. I cleaned the battery connections with + and ground. The car starts and works properly. The clock backlight also lights up. The user manual came in handy . Either the mechanic played a trick on me or the child was playing. I didn't expect the backlight to be adjusted in such a place, or to be turned in such a direction to make it brighter I love this car.