I have similar symptoms on my 97 E320 parts car. ( Limp mode is 2nd and reverse not first. ) Car was built June 96

The drivers info display has some sort of message ( probably bulb out but it has been a while since I ran the car ), high beam indicator stays on and driving lights turn on. The speedo does work but I think it gets a signal from the ABS sensor on the right front wheel. One time everything returned to normal and the trans shifted fine.

I don't recall if any codes were tripped in the trans or engine computer, I'll check next time my other computer is turned on.

My guess is that some sort of CAN connected module is failing and sending the wrong message. There is something called " Bit Rot " where a PROM / EPROM / EEPROM will start to loose internal electrical charges. This results in loss of memory and all sorts of odd behavior. I wonder if that is what is happening here.

The E320 does have a body computer of sorts, I'd like to see if there is some sort on interaction there.

I'm really like to sniff CAN traffic during the issue to see what is happening.

We need, wiring diagrams for the trans and other related systems.