Engine shut off after about 30 mins

[Porschepetter]

My 1976 911S 2.7L has a problem where it shuts off after warming up—about 30 minutes into driving.
The issue started around the same time I noticed the charging light came on. The tachometer has also started jumping. Here’s what I’ve done so far:

I suspected a grounding issue, so I replaced the ground strap from the transmission to the chassis. I also installed a new ignition coil, but the problem persists.

Maybe the alternator is bad and needs to be replaced to provide stable power to the car? As I understand it, the fuel injection system needs steady voltage to function properly?

Another possibility could be the CDI box, but the car starts easily and runs well for about 30 minutes—which it probably wouldn’t if the CDI box were faulty, right?

Does anyone have suggestions for further troubleshooting?