[RICK LAKE]

DanEC Dan let me give you some info on this problem,
First the cobra charging system is limited to 70amps with changing the amp gauge to a voltage gauge. It took 9 years but I melted the insolators on the amp gauge. TOO MUCH AMPAGE going through this gauge. Must cobras run a 63 amp alt. You are at the limit of this gauge. Old days cobra had a 38 to 45 amp charging system The car had headlights, wipers, and 2 fuel pumps, Some had a heater as an option and a battery small one about 500cca At idle the charging system produced about 25-28 amps. enough to cover the Ign system, fuel pumps, and lights. NOt 100% sure about electrical fans like today.
Here's the thing, if you have undersize pulleys on the motor, the charging system can't handle the load. If you are using a Tarus fan, they draw between 18-22 amps at high speed alone. Add the igntion system if MSD another 10 amps, fuel pumps, 4-10 amps. Lights 2-5 amps. Half the total charging system
When you get a chance measure the pulleys on the crank and water pump. IF they are 1-1, ( same size ) you are OK. IF the crank is smaller, you are under size and to have the motor idling below 800-900 rpms you have no charging ampage to the car and all drains are pulling from the battery. THat fan turns on and the surge to turn it on can be 40-60 amps. This is the reason for the amp meter to pin neg side. It will come back in a second or 2.
Bottom line you have 4 choices
1, replace the amp gauge with a volt gauge from autometer. Cost about $60.00 for gauge. Remove screws from dash panel and cock it down to get to gauge. Nut and bolt 2 white wires togeather with a 3rd wire for the voltage gauge. Need a ground wire, and swap the light out of the smith gauge into the back of the auto meter gauge. Take about 1 hour with a screw gun. Solder the connectors. heat wrap seal and tape up. Reassembly dash Make sure wires can't rub on anything. This will pervent a dash fire but not fix the amp load.
2, Pulleys on motor, if not the same size, get the same ones in size. This will help cooling the motor also. This will increase the speed of the alt raise the charging and help decrease the surge load when the fan kicks on. Still will get the spike throught the amp gauge, again same issue as line 1.
3, Replace this fan with a good cfm and lower amp draw. 16" works ok. (Side note) Do you have the 2 little fans in front of the radiator or the deflector shield? This is important. I like the 2 little fans BUT they do nothing in helping direct the air smoothly into the radiator. As what temp thermostat are you running? REcommend a 180F thermostat from an RB dodge motor. Works great with a little grinding to get it to fit in the FE manifold The flow opening is 1/2" larger than the FE one. Makes a big different in cooling the motor.
This will help keep the fan from coming on.
4 PA performance sell a 95 amp kit for a cobra with a voltage box and direct bolt in unit. Also has a 125 amp fusable link to protect encase of a short on this side of the charging system. You will still need a Voltage meter. About $350.00 lifetime warrantty. I run this setup because of 3 cooling fans to motor,2 fuel pumps, ecu, fuel injectors, MSD ignition system, ( this draws about 10 amps ,not the 2-3 that others have said here, I measured the load) lights. I also have a heater but not used. At idle I pull just under 32 amps. My OEM alt of 63 couldn't handle this load and drained the battery at idle and had a hard time recovering when racing. I had to recharge the battery after every run. I had under drive pulleys and went 1-1 ratio. This helped a little
I don't know how you wired this coolant fan but would look into running it directly to the battery and ground and use a signal wire to turn it on and off. THis will pervent the surge to the amp gauge. Over time the plastic insolators are going to fail and need to be replaced. I got 9 years and lucky I caught mine at home in the garage. IT could have burnt the car to the ground on the next outting. Good luck with your problem Sorry from long leter, trying to give you all options for repair. Rick L. Ps as far as charging the needle should read on the pos side between 0 and 30 amps without alot of load. This is with a fully charged battery. The gauge is not that accurate. It's in the ball park. Pss got any pictures of the GTX and info???? Looking for one for a friend.