I installed a CD player in my 1983 300D (W123) and I noticed that the constant hot lead went back under the center console towards the hazard light switch. I peeked under there and sure enough there was a "tap" off of the power feed for the switch. I don't think the factory put a constant hot lead in my car as it only had a cassette player with no clock and would have had no need for one. I think the W124 has the flasher in the same place so you could do this trick if some reason you don't ever get the fuse situ worked out (or there is a short in the lead)...

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~Sugi
1983 300DT
1964 Triumph TR4 (back in the stable after 18 years- same car!)
2004 Pontiac Vibe
1986 Honda Elite CH250
1971 F100