Thank you for letting us know the outcome. Disappointingly some people just drop the thread when they find the solution.
The interesting part of the diagnosis that we often rely on was absent from your description:
" Does the tachometer needle bounce when you crank ?"
In theory ,it will bounce if the fuel pump relay is defective..but
it
will not bounce if the CPS is defective.
The OEM fuel pump relay seems to be Wittrin or KAE a.k.a. KAEHLER # 2.408.120
Porsche part number 996 615 101 00
Price around $10 for a "Made in Germany" from Pelican . It has one of the 4 pins undersize so generic 4 pin 15/40 relay would not be a substitute. Carry a spare?
Pelican Parts - Product Information: 996-615-101-00-M504