I played a bit with the blower controls in my 1985 300D. I used a climate wiring schematic that has been posted here many times (for a 1984 I recall). In my case, the issue was high resistance at the #8 fuse-holder (which likes to melt). In both my cars, I ran a feed wire straight from BATT+ (pushed thru feedthru under battery) and added a 40 A relay so the factory 12 V supply wire just turns on the relay (see post w/ photos). But you may not need that.

You might first focus on the blower relay box, which is the black plastic one above the glove-box. It is just a bunch of relays which get inputs from the TemperatureRegular box next to it to set 1 of 6 (?) blower speeds, by switching in different resistors (engine bay, front passenger side). You can actuate those yourself by applying 12 V to each pin. Monitor that your 12 V supply pin holds. The relay box also gets inputs from the push-button switch. In auto-speed, the temp box has control. In H, one speed is fixed (highest, i.e. no resistor?) and L sets another speed. Perhaps those inputs flow as requests to the temp box (schematic will tell).

I recall the ground for the blower is above the passenger's right foot. If you remove the under-dash panel and glove-box liner, you should see a stud on the right with many brown wires attached.

I might have bypassed the "coolant temp switch lock-out" in the T-stat housing (connect 2 wires together). That avoids blowing cold air on the passengers by disabling the blower until the coolant warms up (German mothers fear drafts cause illness).

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1984 & 1985 CA 300D's
1964 & 65 Mopar's - Valiant, Dart, Newport
1996 & 2002 Chrysler minivans