What pins do I use for UART control on a RUMBA board for tmc2208?
The RUMBA schematic is available on the RUMBA wiki.  


  


From the schematic, I see that UART3 (with +5V logic levels, not RS232) is presented on the EXP3 connector.  I don't know if Marlin firmware can be controlled through a UART other than UART0, which is converted to USB through an FDDI chip.  The Arduino bootloader is not expecting another UART, so you may still need to program it through the USB port (and UART0).