Railmaster.

It is not the DME relay, but as You say, try the easy things first like empty the ash tray!

A914MAN

When I first started having the problems, I checked everything (except the plug wires) and even though one of the coils had just been replaced, I got everything to upgrade to the 993 coil pack. The 993 coils are much better than the oil filled 964 parts

Derek911

The first thing you need to learn when working on a 964 is to listen to people on the forum. Your car is not unique, they all experience the same faults and people here have already found the fix.
Change your coils first!

LM964

Straight swap or other components or changes required?

Jjm4life

Quoted for truth.

JasonAndreas

The water spray bottle in the dark trick really helps to pinpoint high voltage discharge problems like yours. Maybe do a quick visual inspection of the wiring in the engine compartment and if nothing stands out, start the engine and start spritzing?

You can find some instructions for testing your alternator via the Porsche TSB 9402 - Diagnosing Discharged Battery

Gregg-K

Probably worth noting that the visual tests and water spritzing should be done in a darkened place, so you can more easily see any sparks,
... Gregg